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cond-mat/9211004
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] |
Level repulsion in integrable and almost-integrable quantum spin models
|
The repartition of the separation between energy levels of various isotropic S=1/2 antiferromagnetic chains is studied numerically with the aim of investigating the transition from integrable to non-integrable systems. We begin by displaying the level separation distribution of the integrable Bethe chain. Then two non-integrable systems, two coupled chains and a next-nearest-neighbor coupled chain, are studied as a function of the coupling. We examine how the level spacing evolves from the Poisson distribution to the GOE distribution. Finally we consider the Haldane-Shastry $1/r^{2}$ model. A number of conclusions regarding the behaviour and relevance of the level spacing distribution in these spin systems is drawn.
|
Theodore C. Hsu and J.C. Angles d'Auriac
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211004
|
cond-mat/9211005
|
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] |
Spin-Wave Theory of the Spiral Phase of the t-J Model
|
A graded H.P,realization of the SU(2|1) algebra is proposed.A spin-wave theory with a condition that the sublattice magnetization is zero is discussed.The long-range spiral phase is investigated.The spin-spin correlator is calculated.
|
N.I.Karchev and T.S.Hristov
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211005
|
cond-mat/9211006
|
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] |
Cluster Algorithm for Vertex Models
|
We present a new type of cluster algorithm that strongly reduces critical slowing down in simulations of vertex models. Since the clusters are closed paths of bonds, we call it the {\em loop algorithm}. The basic steps in constructing a cluster are the break-up and the freezing of vertices. We concentrate on the case of the F model, which is a subset of the 6-vertex model exhibiting a Kosterlitz-Thouless transition. The loop algorithm is also applicable to simulations of other vertex models and of one and two-dimensional quantum spin systems.
|
H.G. Evertz, G. Lana and M. Marcu
|
cond-mat hep-lat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211006
|
cond-mat/9211007
|
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] |
Singularity spectrum of self-organized criticality
|
I introduce a simple continuous probability theory based on the Ginzburg-Landau equation that provides for the first time a common analytical basis to relate and describe the main features of two seemingly different phenomena of condensed-matter physics, namely self-organized criticality and multifractality. Numerical support is given by a comparison with reported simulation data. Within the theory the origin of self-organized critical phenomena is analysed in terms of a nonlinear singularity spectrum different from the typical convex shape due to multifractal measures.
|
E. Canessa (ICTP-Trieste, Italy)
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211007
|
cond-mat/9211008
|
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] |
Rigid Chiral Membranes
|
Statistical ensembles of flexible two-dimensional fluid membranes arise naturally in the description of many physical systems. Typically one encounters such systems in a regime of low tension but high stiffness against bending, which is just the opposite of the regime described by the Polyakov string. We study a class of couplings between membrane shape and in-plane order which break 3-space parity invariance. Remarkably there is only {\it one} such allowed coupling (up to boundary terms); this term will be present for any lipid bilayer composed of tilted chiral molecules. We calculate the renormalization-group behavior of this relevant coupling in a simplified model and show how thermal fluctuations effectively reduce it in the infrared.
|
Philip Nelson and Thomas Powers
|
cond-mat hep-th
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211008
|
cond-mat/9211009
|
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] |
The fermion sign problem: A new decoupling transformation, and a new simulation algorithm
|
We discuss the Fermion sign problem and, by examining a very general Hubbard-Stratonovich (HS) transformation, argue that the sign problem cannot be solved with such methods. We propose a different kind of transformation which, while not solving the sign problem, shows more detailed information about the system. With our transformation it is {\it trivial} to tell which auxiliary field configurations give a positive sign and which give a negative sign. We then discuss briefly various properties of this transformation and construct a new algorithm which with one simulation gives results for a whole range of particle densities and Hubbard $U$ values, positive and negative. Our approach is in excellent agreement with exact calculations.
|
Ghassan George Batrouni and Philippe de Forcrand
|
cond-mat hep-lat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211009
|
cond-mat/9211010
|
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] |
The half-filled Hubbard model in the pair approximation of the Cluster Variation Method
|
The half filled Hubbard model is studied in the pair approximation of the Cluster Variation Method. The use of the $SO(4)$ symmetry of the model makes possible to give a complete analytical characterization of the ground state, by means of explicit expressions for the double occupancy and the nearest neighbor correlation functions. The finite temperature analysis is reduced to the numerical solution of only two coupled transcendental equations. The behavior of local magnetic moment, specific heat and correlation functions is given for some typical cases in one and two dimensions. We obtain good qualitative agreement with exact and numerical results in one dimension. The results for finite temperatures show a rapid evolution, with increasing temperature, from a strongly antiferromagnetic behavior to a disordered one; in the high temperature region a maximum (which has been related to a "gradual" metal--insulator transition) is found in the specific heat for very large values of the Coulomb repulsion.
|
Alessandro Pelizzola
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211010
|
cond-mat/9211011
|
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] |
On the Thermodynamics of Granular Media
|
A thermodynamic formulation for moving granular material is proposed. The fluctuations due to the constant flux and dissipation of energy are controlled in a `granular' ensemble by a pressure $\wp$ (`compression') which is conjugate to a contact volume (`contactopy'). The corresponding response function (`dissipativity') describes how dissipation increases with $\wp$ and should serve to identify the fluidization transition and 1/f noise. In the granular ensemble one can consider the granular medium as a gas of elastically colliding particles and define a ``granular'' temperature and other standard thermodynamic quantities. PACS: 05.70, 46.10
|
H.J. Herrmann
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211011
|
cond-mat/9211012
|
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] |
Second-Order Dynamics in the Collective Evolution of Coupled Maps and Automata
|
We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.
|
P.-M. Binder, V. Privman
|
cond-mat hep-lat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211012
|
cond-mat/9211013
|
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] |
Granular Material Flowing Down an Inclined Chute: A Molecular Dynamics Simulation
|
Two-dimensional Molecular Dynamics simulations are used to model the free surface flow of spheres falling down an inclined chute. The interaction between the particles in our model is assumed to be subjected to the Hertzian contact force and normal as well as shear friction. The stream of particles shows a characteristic height profile, consisting of layers of different types of fluidization. The numerically observed flow properties agree qualitatively with experimental results.
|
Thorsten Poeschel
|
cond-mat hep-lat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211013
|
cond-mat/9211014
|
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] |
Spin-Peierls ground states and frustration in a multi-band Peierls-Hubbard model
|
We discuss the consequences of including both electron-phonon and electron-electron couplings in multi-band models, focusing on numerical studies of a one-dimensional two-band model in the intermediate regime for both coupling strengths. Spin-Peierls as well as long-period, frustrated ground states are identified, reminisent of those found in antiferromagnetic next-nearest neighbor (ANNNI) models. We speculate on experimentally observable signatures of this rich phase diagram. 1992 PACS: 75.30.Fv, 71.45.Lr, 71.38+i, 64.70.Rh
|
H. Roeder, A.R. Bishop, and J. Tinka Gammel
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211014
|
cond-mat/9211015
|
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] |
Cellular automaton for the fracture of disordered media
|
We study numerically the growth of a crack in an elastic medium under the influence of a travelling shockwave. We describe the implementation of a fast algorithm which is perfectly suited for a data parallel computer. Using large scale simulations on the Connection Machine we generate cracks with more than 10000 sites on a $\scriptstyle 1024 \times 1024$ lattice. We show that the resulting patterns are fractal with a fractal dimension that depends on the chosen breaking criterion and varies between $\scriptstyle 1.$ and $\scriptstyle 2.$
|
Peter Ossadnik
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211015
|
cond-mat/9211016
|
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] |
Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles
|
We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable pile.
|
Jysoo Lee and Hans J. Herrmann
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211016
|
cond-mat/9211017
|
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] |
Possible Quantum Spin Liquid States on the Triangular and Kagome Lattices
|
The frustrated spin-one-half Heisenberg model on triangualr and Kagome Lattices is mapped onto a single specis of fermion carrying statistical flux. The corresponding Chern-Simons gauge theory is analyzed at the Gaussian level and found to be massive. This provides a new motivation for the spin-liquid Kalmeyer-Laughlin wave function. Good overlap of this wave function with the numerical ground state is found for small clusters.
|
Kun Yang, K. L. Warman, and S. M. Girvin
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211017
|
cond-mat/9211018
|
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] |
I-V Characteristics of High Temperature Superconductors with Columnar Defects
|
The vortex glass transition in the presence of columnar defects is studied by Monte Carlo simulations of a vortex loop model, suggested by the analogy to the $T=0$ superconductor-insulator transition for dirty bosons in (2+1)D. From finite-size scaling analysis of the $I$-$V$ characteristic we find two dynamical exponents describing the non-equilibrium behavior. We obtain $z_{\perp} = 6 \pm 0.5$ and $z_{\parallel} = 4 \pm 0.5$ when the current is applied perpendicular and parallel to the columnar defects respectively.
|
M. Wallin and S. M. Girvin
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211018
|
cond-mat/9211019
|
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] |
Quantum Mechanics and Superconductivity in a Magnetic Field
|
The influence of a magnetic field on superconductivity is usually described either phenomenologically, using Ginzburg-Landau theory, or semiclassically using Gor'kov theory. In this article we discuss the influence of magnetic fields on the mean-field theory of the superconducting instability from a completely quantum mechanical point of view. The suppression of superconductivity by an external magnetic field is seen in this more physically direct picture to be due to the impossibility, in quantum mechanics, of precisely specifying both the center-of-mass state of a pair and the individual electron kinetic energies. We also discuss the possibility of novel aspects of superconductivity at extremely strong magnetic fields where recent work has shown that the transition temperature may be enhanced rather than suppressed by a magnetic field and where a quantum treatment is essential.
|
A. H. MacDonald, Hiroshi Akera and M.R. Norman
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211019
|
cond-mat/9211020
|
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] |
Diffusion and spectral dimension on Eden tree
|
We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an Eden tree). Finite-size induced crossovers are observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behavior appears to be complicated and dependent on dimension even qualitatively.
|
Hisao Nakanishi and Hans J. Herrmann
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211020
|
cond-mat/9211021
|
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] |
Magnetic Oscillations of a Fractional Hall Dot
|
We show that a quantum dot in the fractional Hall regime exhibits mesoscopic magnetic oscillations with a period which is a multiple of the period for free electrons. Our calculations are performed for parabolic quantum dots with hard-core electron-electron interactions and are exact in the strong field limit for $k_B T$ smaller than the fractional Hall gap. Explicit expressions are given for the temperature dependence of the amplitude of the oscillations.
|
A.H.MacDonald and M.D. Johnson
|
cond-mat
|
November
| 1,992 |
https://arxiv.org/abs/cond-mat/9211021
|
cond-mat/9212001
|
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] |
The Mass Gap of the Nonlinear Sigma Model through the Finite Temperature Effective Action
|
The $O(3)$ nonlinear $\sigma$ model is studied in the disordered phase, using the techniques of the effective action and finite temperature field theory. The nonlinear constraint is implemented through a Lagrange multiplier. The finite temperature effective potential for this multiplier is calculated at one loop. The existence of a nontrivial minimum for this potential is the signal of a disordered phase in which the lowest excited state is a massive triplet. The mass gap is easily calculated as a function of temperature in dimensions 1, 2 and 3. In dimension 1, this gap is known as the Haldane gap, and its temperature dependence is compared with experimental results.
|
D. Senechal
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212001
|
cond-mat/9212002
|
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] |
Weak-Localization and Integrability in Ballistic Cavities
|
We demonstrate the existence of an interference contribution to the average magnetoconductance, G(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G(B) is qualitatively different for chaotic and regular cavities, an effect explained semiclassically by the differing classical distribution of areas. The magnitude of G(B) is poorly explained by the semiclassical theory of coherent backscattering (elastic enhancement factor)-- correlations beyond time-reversed pairs of trajectories must be included-- but is in agreement with random matrix theory.
|
H. U. Baranger, R. A. Jalabert, and A. D. Stone
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212002
|
cond-mat/9212003
|
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] |
Recurrent Clogging and Density Waves in Granular Material Flowing through a Narrow Pipe
|
We report on density waves in granular material, investigated both experimentally and numerically. When granular material falls through a long narrow pipe one observes recurrent clogging. The kinetic energy of the falling particles increases up to a characteristic threshold corresponding to the onset of recurrent clogging and density waves of no definite wavelength. The distances between regions of high density depend strongly on the initial conditions. They vary irregularly without any characteristic time and length scale. The particle-flow was investigated using 2D Molecular Dynamics simulations. Experimental investigations lead to equivalent results.
|
Thorsten Poeschel
|
cond-mat hep-lat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212003
|
cond-mat/9212004
|
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] |
Fractal Properties of the Distribution of Earthquake Hypocenters
|
We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four different sets of data for the hypocenter distributions and calculating the dynamical properties of the geometrical distribution such as the spectral dimension $d_s$. We find that the value of $d_s$ is consistent with that of the backbone, thus supporting further the identification of the hypocenter distribution as having the structure of the percolation backbone.
|
Hisao Nakanishi, Muhammad Sahimi, Michelle C. Robertson, Charles C. Sammis and Mark D. Rintoul
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212004
|
cond-mat/9212005
|
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] |
Length-scale competition in the damped sine-Gordon chain
|
It is shown that there are two different regimes for the damped sine-Gordon chain driven by the spatio-temporal periodic force $\Gamma sin(\omega t - k_{n} x)$ with a flat initial condition. For $\Gamma_{c}(n)$ to a translating {\em 2-breather} excitation from a state locked to the driver. For $\omega < k_{n}$, the excitations of the system are the locked states with the phase velocity $\omega/k_{n}$ in all the region of $\Gamma$ studied. In the first regime, the frequency of the breathers is controlled by $\omega$, and the velocity of the breathers, controlled by $k_{n}$, is shown to be the group velocity determined from the linear dispersion relation for the sine-Gordon equation. A linear stability analysis reveals that, in addition to two competing length-scales, namely, the width of the breathers and the spatial period of the driving, there is one more length-scale which plays an important role in controlling the dynamics of the system at small driving. In the second regime the length-scale $k_{n}$ controls the excitation. The above picture is further corroborated by numerical nonlinear spectral analysis. An energy balance estimate is also presented and shown to predict the critical value of $\Gamma$ in good agreement with the numerics.
|
David Cai (1), A.R. Bishop (1), and Angel Sanchez (1,2) ((1) Theoretical Division and CNLS, Los Alamos National Laboratory...
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212005
|
cond-mat/9212006
|
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] |
A determination of the low energy parameters of the 2-d Heisenberg antiferromagnet
|
We perform numerical simulations of the 2-d antiferromagnetic quantum Heisenberg model using an efficient cluster algorithm. Comparing the finite size and finite temperature effects of various quantities with recent results from chiral perturbation theory we are able to determine the low energy parameters of the system very precisely. We find $e_0 = - 0.6693(1) J/a^2$ for the ground state energy density, ${\cal M}_s = 0.3074(4)/a^2$ for the staggered magnetization, $\hbar c = 1.68(1) J a$ for the spin wave velocity and $\rho_s = 0.186(4) J$ for the spin stiffness. Our results agree with experimental data for the undoped precursor insulators of high-$T_c$ superconductors.
|
U.-J. Wiese and H.-P. Ying, (Bern University)
|
cond-mat hep-lat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212006
|
cond-mat/9212007
|
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] |
Low Temperature Transport through a Quantum Dot: The Anderson Model out of Equilibrium
|
NEC technical report 92-079-2-0077-1.
|
Y. Meir, N. S. Wingreen and P. A. Lee
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212007
|
cond-mat/9212008
|
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] |
Indications of d_{x^2 - y^2} Superconductivity in the Two Dimensional t-J Model
|
Superconducting correlations in the two dimensional ${\rm t-J}$ model at zero temperature are evaluated using numerical techniques. At the fermionic density $\langle n \rangle \sim 1/2$, strong signals of $\dx2y2$ superconductivity were observed in the ground state. These conclusions are based on a study of static pairing correlations, the Meissner effect, flux quantization, and other indicators of superconductivity. It is argued that these results can be explained using a spin dimer ``liquid'' state. A phase diagram of the two dimensional ${\rm t-J}$ model is presented.
|
Elbio Dagotto and Jose Riera
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212008
|
cond-mat/9212009
|
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] |
Basis Set Reduction Applied to the Two Dimensional t-Jz Model
|
A simple variation of the Lanczos method is discussed. The new technique is based on a systematic reduction of the size of the Hilbert space of the model under consideration. As an example, the two dimensional ${\rm t-J_z}$ model of strongly correlated electrons is studied. Accurate results for the ground state energy can be obtained on clusters of up to 50 sites, which are unreachable by conventional Lanczos approaches. In particular, the energy of one and two holes is analyzed as a function of ${\rm J_z/t}$. In the bulk limit, it is shown that a finite coupling ${\rm J_z/t ]_c} \sim 0.18$ is necessary to induce ``binding'' of holes in the model. It is argued that this result implies that the two dimensional ${\rm t-J}$ model phase separates only for couplings larger than a $finite$ critical value.
|
Jose Riera and Elbio Dagotto
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212009
|
cond-mat/9212010
|
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] |
Dynamical Properties of a Single Hole in an Antiferromagnet
|
A finite size scaling analysis of the spectral function and of the optical conductivity of a single hole moving in an antiferromagnetic background is performed. It is shown that both the low energy quasiparticle peak and the broad higher energy structure are robust with increasing cluster size from $4\times 4$ to $\sqrt{26}\times\sqrt{26}$ sites. In the abscence of spin fluctuations, for most static or dynamical quantities saturation occurs when the size exceeds a characteristic size $N_c(J_z)$. Typically, 16 and 26 site clusters give reliable results for $J_z>0.75$ and $J_z>0.3$ respectively. The hole optical mass is shown to be very large ($>20$) in agreement with the small bandwidth. Due to the energy gap to flip a spin in the vicinity of a hole, a small gap $\propto J_z$ separates the low energy delta-function from the rest of the spectrum in the dynamical correlation functions. On the other hand, with $J_\perp$ this gap seems to disappear with increasing system size as one would expect since the spin waves are gapless in the thermodynamic limit. The large momentum dependence of the quasiparticle weight in the isotropic case is inconsistent with a string picture but agrees well with the self-consistent Born approximation. An accurate estimation of the higher energy part of the spectral functions of the t--J model can be made for momenta close to $(0,0)$ or $(\pi,\pi)$;
|
Didier Poilblanc, Timothy Ziman, H.J. Schulz and Elbio Dagotto
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212010
|
cond-mat/9212011
|
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] |
Translational Correlations in the Vortex Array at the Surface of a Type-II Superconductor
|
We discuss the statistical mechanics of magnetic flux lines in a finite-thickness slab of type-II superconductor. The long wavelength properties of a flux-line liquid in a slab geometry are described by a hydrodynamic free energy that incorporates the boundary conditions on the flux lines at the sample's surface as a surface contribution to the free energy. Bulk and surface weak disorder are modeled via Gaussian impurity potentials. This free energy is used to evaluate the two-dimensional structure factor of the flux-line tips at the sample surface. We find that surface interaction always dominates in determining the decay of translational correlations in the asymptotic long-wavelength limit. On the other hand, such large length scales have not been probed by the decoration experiments. Our results indicate that the translational correlations extracted from the analysis of the Bitter patterns are indeed representative of behavior of flux lines in the bulk.
|
M.C. Marchetti (Syracuse University) and D.R. Nelson (Harvard University)
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212011
|
cond-mat/9212012
|
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] |
Exact Correlation Function at the Lifshitz Points of the Spherical Model
|
The spin-spin correlation function of the spherical model being precisely at an anisotropic Lifshitz point of arbitrary order is calculated exactly. The results are in agreement with scaling. The scaling function is shown to be universal. The direction-dependent long-range correlations may change from ferromagnetic to antiferromagnetic behaviour and back as the dimension is varied. The form of the scaling function is compared to predictions following from local scale invariance for strongly anisotropic critical systems.
|
Laurent Frachebourg and Malte Henkel
|
cond-mat hep-lat hep-th math-ph math.MP
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212012
|
cond-mat/9212013
|
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] |
Bosonic Mean Field Theory of the Spiral Phases of Heisenberg Antiferromagnets on a Chain
|
We develop a novel bosonic mean field theory to describe the spiral phases of a Heisenberg antiferromagnet on a one-dimensional chain, in terms of three bosons at each site. The ground state is disordered and for large values of the spin $S$, two different and exponentially small energy gaps are found. The spin-spin correlation function is computed and is shown to decay exponentially at large distances. Our mean field theory is also shown to be exact in a large-$N$ generalization.
|
Sumathi Rao and Diptiman Sen
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212013
|
cond-mat/9212014
|
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] |
Dynamical Properties of a Haldane Gap Antiferromagnet
|
We study the dynamic spin correlation function of a spin one antiferromagnetic chain with easy-plane single-ion anisotropy. We use exact diagonalization by the Lancz\H os method for chains of lengths up to N=16 spins. We show that a single-mode approximation is an excellent description of the dynamical properties. A variational calculation allows us to clarify the nature of the excitations. The existence of a two-particle continuum near zero wavevector is clearly seen both in finite-size effects and in the dynamical structure factor. The recent neutron scattering experiments on the quasi-one-dimensional antiferromagnet NENP are fully explained by our results.
|
O. Golinelli, Th. Jolicoeur, R. Lacaze
|
cond-mat hep-lat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212014
|
cond-mat/9212015
|
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] |
Theory of Anisotropic Superexchange in Insulating Cuprates
|
Spin-orbit corrections to superexchange are calculated using the method of Moriya [T.\ Moriya, {\it Phys.\ Rev.}~{\bf 120} 91, (1960)] for two of the insulating parent compounds of the cuprate superconductors: (1) La$_{2-x}$Nd$_x$CuO$_4$ where the CuO$_6$ octahedra forming each Cu-O layer are tilted in staggered fashion about an axis which depends on $x$ and temperature; and (2) YBa$_2$Cu$_3$O$_{6+x}$ ($x \alt 0.4$) where the Cu-O layers form CuO$_2$-Y-CuO$_2$ bilayers in which the in-plane O$^{2-}$ ions are displaced uniformly towards the Y$^{3+}$ layer. For (1) a simple formula is derived for the weak ferromagnetic moment in each Cu-O layer as a function of the tilting axis and magnitude. For (2) it is shown that the anisotropic corrections to superexchange are different from what has previously been assumed. For the correct spin Hamiltonian a classical N\'eel state in which the Cu spins are lying in the plane is unstable in a single Cu-O layer, but when a bilayer is considered there is a critical value of the interlayer exchange coupling which stabilizes this state. For both cases (1) and (2) spin-wave spectra are calculated and shown to compare favorably with experiment.
|
N.E. Bonesteel
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212015
|
cond-mat/9212016
|
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] |
Tunneling Conductance Between Parallel Two Dimensional Electron Systems
|
We derive and evaluate expressions for the low temperature {\it dc} equilibrium tunneling conductance between parallel two-dimensional electron systems. Our theory is based on a linear-response formalism and on impurity-averaged perturbation theory. The disorder broadening of features in the dependence of tunneling conductance on sheet densities and in-plane magnetic field strengths is influenced both by the finite lifetime of electrons within the wells and by non-momentum-conserving tunneling events. Disorder vertex corrections are important only for weak in-plane magnetic fields and strong interwell impurity-potential correlations. We comment on the basis of our results on the possibility of using tunneling measurements to determine the lifetime of electrons in the quantum wells.
|
Lian Zheng and A.H. MacDonald
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212016
|
cond-mat/9212017
|
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] |
Flux Pinning and Phase Transitions in Model High-Temperature Superconductors with Columnar Defects
|
We calculate the degree of flux pinning by defects in model high-temperature superconductors (HTSC's). The HTSC is modeled as a three-dimensional network of resistively-shunted Josephson junctions in an external magnetic field, corresponding to a HTSC in the extreme Type-II limit. Disorder is introduced either by randomizing the coupling between grains (Model A disorder) or by removing grains (Model B disorder). Three types of defects are considered: point disorder, random line disorder, and periodic line disorder; but the emphasis is on random line disorder. Static and dynamic properties of the models are determined by Monte Carlo simulations and by solution of the analogous coupled overdamped Josephson equations in the presence of thermal noise. Random line defects considerably raise the superconducting transition temperature T$_c(B)$, and increase the apparent critical current density J$_c(B,T)$, in comparison to the defect-free crystal. They are more effective in these respects than a comparable volume density of point defects, in agreement with the experiments of Civale {\it et al}. Periodic line defects commensurate with the flux lattice are found to raise T$_c(B)$ even more than do random line defects. Random line defects are most effective when their density approximately equals the flux density. Near T$_c(B)$, our static and dynamic results appear consistent with the anisotropic Bose glass scaling hypotheses of Nelson and Vinokur, but with possibly different critical indices:
|
K. H. Lee, D. Stroud, and S. M. Girvin
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212017
|
cond-mat/9212018
|
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] |
Spin Tunneling, Berry phases and Doped Antiferromagnets
|
Interference effects between Berry phase factors in spin tunneling systems have been discussed in recent Letters by Loss, DiVincenzo and Grinstein and von Delft and Henley. This Comment points out that Berry phases in spin tunneling are important in another interesting case: the two dimensional doped antiferromagnet. I show that the dispersion of a single hole in the t-J model changes sign as $e^{2\pi s}$ where $s$ is the size of the spins. This provides an interpretation of the numerical results for the $s=\half$ model, and a prediction for other spin sizes.
|
Assa Auerbach
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212018
|
cond-mat/9212019
|
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] |
The $1/N$ Expansion and Spin Correlations in Constrained Wavefunctions
|
We develop a large-N expansion for Gutzwiller projected spin states. We consider valence bonds singlets, constructed by Schwinger bosons or fermions, which are variational ground states for quantum antiferromagnets. This expansion is simpler than the familiar expansions of the quantum Heisenberg model, and thus more instructive. The diagrammatic rules of this expansion allow us to prove certain identities to all orders in 1/N. We derive the on-site spin fluctuations sum rule for arbitrary N. We calculate the correlations of the one dimensional Valence Bonds Solid states and the Gutzwiller Projected Fermi Gas upto order 1/N. For the bosons case, we are surprised to find that the mean field, the order 1/N and the exact correlations are simply proportional. For the fermions case, the 1/N correction enhances the zone edge singularity. The comparison of our leading order terms to known results for N=2, enhances our understanding of large-N approximations in general.
|
Maxim Raykin (Physics Department, Boston University, Boston, USA) and Assa Auerbach (Physics Department, Technion, Haifa, ...
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212019
|
cond-mat/9212020
|
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] |
Spin-Wave Theory and Finite-Size Scaling for the Heisenberg Antiferromagnet
|
Spin-wave perturbation theory for the Heisenberg antiferromagnet at zero temperature is used to compute the finite-lattice corrections to the ground state energy, the staggered magnetization and the energy gap. The dispersion relation, the spin-wave velocity and the bulk ground state energy to order $O(1/S^2)$ are also computed for the square lattice. The results agree very well with the predictions of Neuberger and Ziman and Fisher.
|
Zheng Weihong and C.J. Hamer
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212020
|
cond-mat/9212021
|
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] |
Test of Conformal Invariance in One-Dimensional Quantum Liquid with Long-Range Interaction
|
We numerically study the momentum distribution of one-dimensional Bose and Fermi systems with long-range interaction $g/r^2$ for the ``special'' values $g= -\frac{1}{2}, 0, 4$, singled out by random matrix theory. The critical exponents are shown to be independent of density and in excellent agreement with estimates obtained from $c=1$ conformal finite-size scaling analysis.
|
Rudolf A. R\"omer and Bill Sutherland
|
cond-mat hep-th
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212021
|
cond-mat/9212022
|
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] |
Electronic interactions in fullerene spheres
|
The electron-phonon and Coulomb interactions inC$_{60}$, and larger fullerene spheres are analyzed. The coupling between electrons and intramolecular vibrations give corrections $\sim 1 - 10$ meV to the electronic energies for C$_{60}$, and scales as $R^{-4}$ in larger molecules. The energies associated with electrostatic interactions are of order $\sim 1 - 4$ eV, in C$_{60}$ and scale as $R^{-1}$. Charged fullerenes show enhanced electron-phonon coupling, $\sim 10$ meV, which scales as $R^{-2}$. Finally, it is argued that non only C$_{60}^{-}$, but also C$_{60}^{--}$ are highly polarizable molecules. The polarizabilities scale as $R^3$ and $R^4$, respectively. The role of this large polarizability in mediating intermolecular interactions is also discussed.
|
F. Guinea, J. Gonzalez and M.A. H. Vozmediano
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212022
|
cond-mat/9212023
|
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] |
Scaling Exponents for Kinetic Roughening in Higher Dimensions
|
We discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d=7+1. To this end, we study the restricted solid - on - solid growth model, for which we employ a novel fitting {\it ansatz} for the spatially averaged height correlation function $\bar G(t) \sim t^{2\beta}$ to estimate the scaling exponent $\beta$. Using this method, we present a quantitative determination of $\beta$ in d=3+1 and 4+1 dimensions. To check the consistency of these results, we also compute the interface width and determine $\beta$ and $\chi$ from it independently. Our results are in disagreement with all existing theories and conjectures, but in four dimensions they are in good agreement with recent simulations of Forrest and Tang [{\it Phys. Rev. Lett.} {\bf 64}:1405 (1990)] for a different growth model. Above five dimensions, we use the time dependence of the width to obtain lower bound estimates for $\beta$. Within the accuracy of our data, we find no indication of an upper critical dimension up to d=7+1.
|
T. Ala-Nissila, T. Hjelt, J. M. Kosterlitz, and O. Ven\"al\"ainen
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212023
|
cond-mat/9212024
|
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] |
Multiscaling analysis and width of the active zone of large off-lattice DLA
|
We measure the multiscaling behavior of large off-lattice diffusion limited aggregates (DLA). In contrast to previous studies we now find a continuous dependence of the multiscaling dimensions $D(x)$ on the relative distance $x=r/R_g$ to the center of the cluster. This result agrees with measurements on smaller clusters. Furthermore we report the multiscaling behavior and the behavior of the width of the active zone of one very large off-lattice DLA cluster with 50 million particles. Here we find a sharp drop of the multiscaling dimensions for large $x$ instead of a continuous behavior.
|
Peter Ossadnik
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212024
|
cond-mat/9212025
|
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] |
Fractional Quantum Hall States in Narrow Channels
|
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical diagonalization of the Hamiltonian. It is shown that the fractional quantum Hall states are realized even in the presence of the external potential under suitable conditions, and a phase diagram is obtained.
|
Daijiro Yoshioka
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212025
|
cond-mat/9212026
|
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] |
On Oscillations in Cellular Automata
|
We investigate cellular automata where some global quantity varies periodically or quasiperiodically with time. We find that these systems are highly predictable, and can be rather well described by a set of mean-field variables. We conclude that this is not a collective phenomenon - where different subsystems are supposed to synchronize - but rather like many very weakly coupled oscillators fluctuating around one exact frequency. The global quantity measured is a mean taken over all these subsystems, and gets more precise the larger the system is.
|
Jan Hemmingsson and Hans J. Herrmann
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212026
|
cond-mat/9212027
|
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] |
A Solvable Spin-Glass of Quantum Rotors
|
We examine a model of $M$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. A complete solution is obtained at $M=\infty$ in the spin-glass and quantum-disordered phases. The quantum phase transition separating them is found to possess logarithmic violations of scaling, with no further modifications to the leading critical behavior at any order in $1/M$; this suggests that the critical properties of the transverse-field Ising model (believed to be identical to the $M\rightarrow 1$ limit) are the same as those of the $M=\infty$ quantum rotors.
|
Jinwu Ye, Subir Sachdev, and N. Read
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212027
|
cond-mat/9212028
|
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] |
Solution of Some Integrable One-Dimensional Quantum Systems
|
In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics. The periodic inverse square case is worked out explicitly. Next, we show that in the limit of strong interaction the "spin" degrees of freedom decouple. Taking this limit for our example, we obtain a complete solution to a lattice system introduced recently by Shastry, and Haldane; our solution reproduces the numerical results. Finally, we emphasize the simple explanation for the high multiplicities found in this model.
|
Bill Sutherland, B. Sriram Shastry (Physics Department, AT&T Bell Labs, Murray Hill, NJ and University of Utah, Salt Lake ...
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212028
|
cond-mat/9212029
|
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] |
Super Lax Pairs and Infinite Symmetries in The $1/r^2$ System
|
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2 $ family of interactions. The algebra consists of the commutation between a ``Super- Hamiltonian'', and two other operators, in a Hilbert space that is an enlargement of the original one by introducing fermions. The commutation relations reduce to quantal Ordered Lax equations when projected to the original subspace, and to a statement about the ``Harmonic Lattice Potential'' structure of the Lax operator. These in turn lead to a highly automatic proof of the integrability of these models. In the case of the discrete $SU(n)-1/r^2$ model, the `` Super-Hamiltonian'' is again an $SU(m)-1/r^2$ model with a related $m$, providing an interesting hierarchy of models.
|
B. Sriram Shastry (AT & T Bell Laboratories, Murray Hill, N.J.) and Bill Sutherland (Department of Physics,University of U...
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212029
|
cond-mat/9212030
|
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] |
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
|
We examine the spin-$S$ quantum Heisenberg magnet with Gaussian-random, infinite-range exchange interactions. The quantum-disordered phase is accessed by generalizing to $SU(M)$ symmetry and studying the large $M$ limit. For large $S$ the ground state is a spin-glass, while quantum fluctuations produce a spin-fluid state for small $S$. The spin-fluid phase is found to be generically gapless - the average, zero temperature, local dynamic spin-susceptibility obeys $\bar{\chi} (\omega ) \sim \log(1/|\omega|) + i (\pi/2) \mbox{sgn} (\omega)$ at low frequencies. This form is identical to the phenomenological `marginal' spectrum proposed by Varma {\em et. al.\/} for the doped cuprates.
|
Subir Sachdev and Jinwu Ye
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212030
|
cond-mat/9212031
|
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] |
Spin Gap and Superconductivity in the One-Dimensional t-J Model with Coulomb Repulsion
|
The one-dimensional t-J model with density-density repulsive interactions is investigated using exact diagonalization and quantum Monte Carlo methods. A short-range repulsion pushes phase separation to larger values of J/t, and leads to a widened precursor region in which a spin gap and strengthened superconducting correlations appear. The correlation exponent is calculated. On the contrary, a long-range repulsion of $1/r$-form suppresses superconductivity in the precursor region.
|
M.Troyer, H. Tsunetsugu, T.M. Rice, J. Riera and E. Dagotto
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212031
|
cond-mat/9212032
|
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] |
Spatial Correlation of Conduction Electrons in Metal with Complicated Geometry Of The Fermi Surface
|
The "density-density" correlation function of conduction electrons in metal is investigated. It is shown, that the asymptotic behaviour of the CF depends on the shape and the local geometry of the Fermi surface. In particular, the exponent of power law which describes the damping of Friedel oscillations at large r (-4 for an isotropic Fermi gas) is determined by local geometry of the FS. The applications of the obtained results to calculations of the CF in a metal near the electron topological transition and of the RKKY exchange integral are considered as well.
|
D.I.Golosov and M.I.Kaganov
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212032
|
cond-mat/9212033
|
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] |
Hierarchical Wave Functions and Fractional Statistics in Fractional Quantum Hall Effect on the Torus
|
One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.
|
Dingping Li
|
cond-mat hep-th
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212033
|
cond-mat/9212034
|
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1.818885087966919,
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0.1668904423713684,
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] |
Hierarchical Wave Functions of Fractional Quantum Hall Effect on the Torus
|
One kind of the hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions closely relate to the wave functions of generalized Abelian Chern-Simons theory.
|
Dingping Li
|
cond-mat hep-th
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212034
|
cond-mat/9212035
|
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] |
On flux phase and N\'eel antiferromagnetism in the {\em t}-{\em J}-model}}
|
We reanalyse the mathematical formulation of the flux-state problem within the $t$-$J$ model. The analysis of different parametrizations in the functional representation shows that (i) calculations which take into account constraints for the number of on-site-available states are describing quasiparticles in terms of wrong local statistics, and contain gauge non-invariant objects; (ii) application of the projection technique in the slave-boson(fermion) representation reproduces the correct statistics, and is exactly equivalent to the conventional diagram technique for Hubbard operators; (iii) it is necessary to introduce an additional equation for the effective hopping amplitude for the flux phase. With the technique for Hubbard operators, which allows one to separate charge and spin channels we construct the mean-field equations for a flux-like state which coexists with N\'eel antiferromagnetism (AF). The formal analysis shows that the equations for real and imaginary parts of the effective hopping amplitude are inconsistent for any $\theta \neq 0$ (including $\theta =\pi /4$ which gives flux 1/2). The hopping amplitude is slightly supressed by exchange renormalization. The N\'eel magnetization $m$ decreases with increasing concentration of holes. The region where antiferromagnetism exists is decreasing
|
I.S. Sandalov, M. Richter
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212035
|
cond-mat/9212036
|
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] |
Dimerization structures on the metallic and semiconducting fullerene tubules
|
The Kekule patterns are realized in the metallic tubules and chain-like distortions occur in the semiconducting tubules.
|
Kikuo Harigaya (1) and Mitsutaka Fujita (2) ((1)Department of Physics, University of Sheffield, United Kingdom, (2) Instit...
|
cond-mat
|
December
| 1,992 |
https://arxiv.org/abs/cond-mat/9212036
|
funct-an/9205001
|
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] |
A Baire Category Approach to the Bang-Bang Property
|
Aim of this paper is to develop a new technique, based on the Baire category theorem, in order to establish the closure of reachable sets and the existence of optimal trajectories for control systems, without the usual convexity assumptions. The bang-bang property is proved for a new class of ``concave" multifunctions, characterized by the existence of suitable linear selections. The proofs rely on Lyapunov's theorem in connection with a Baire category argument.
|
Alberto Bressan and Benedetto Piccoli
|
funct-an math.FA
|
May
| 1,992 |
https://arxiv.org/abs/funct-an/9205001
|
funct-an/9205002
|
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] |
Integral representation for a class of $C^1$-convex functionals
|
In view of the applications to the asymptotic analysis of a family of obstacle problems, we consider a class of convex local functionals $F(u,A)$, defined for all functions $u$ in a suitable vector valued Sobolev space and for all open sets $A$ in ${\bf R}^n$. Sufficient conditions are given in order to obtain an integral representation of the form $F(u,A)=\int_A f(x,u(x))\,d\mu + \nu(A)$, where $\mu$ and $\nu$ are Borel measures and $f$ is convex in the second variable.
|
Gianni Dal Maso, Anneliese Defranceschi, Enrico Vitali
|
funct-an math.FA
|
May
| 1,992 |
https://arxiv.org/abs/funct-an/9205002
|
funct-an/9205003
|
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Nonstandard hulls of Banach-Lie groups and algebras
|
We propose a new construction of Banach-Lie groups and algebras relying on nonstandard analysis. A major standard application is the Local Theorem which to certain extent reduces the problem of associating a Lie group to a given banach-Lie algebra to a similar problem for finitely generated Lie subalgebras. We discuss possible applications, e.g., to gauge theories.
|
Vladimir G. Pestov
|
funct-an math.OA
|
May
| 1,992 |
https://arxiv.org/abs/funct-an/9205003
|
funct-an/9208001
|
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] |
Universal arrows to forgetful functors from categories of topological algebra
|
We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and much more. An accent is put on relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and others may hopefully become amenable to methods of this theory.
|
Vladimir G. Pestov
|
funct-an math.OA
|
August
| 1,992 |
https://arxiv.org/abs/funct-an/9208001
|
funct-an/9209001
|
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] |
Extremal Selections of Multifunctions Generating a Continuous Flow
|
Let $F:[0,T]\times\R^n\mapsto 2^{\R^n}$ be a continuous multifunction with compact, not necessarily convex values. In this paper, we prove that, if $F$ satisfies the following Lipschitz Selection Property: \begin{itemize} \item[{(LSP)}] {\sl For every $t,x$, every $y\in \overline{co} F(t,x)$ and $\varepsilon>0$, there exists a Lipschitz selection $\phi$ of $\overline{co}F$, defined on a neighborhood of $(t,x)$, with $|\phi(t,x)-y|<\varepsilon$.} \end{itemize} then there exists a measurable selection $f$ of $ext F$\ such that, for every $x_0$, the Cauchy problem $$ \dot x(t)=f(t,x(t)),\qquad\qquad x(0)=x_0 $$ has a unique Caratheodory solution, depending continuously on $x_0$. We remark that every Lipschitz multifunction with compact values satisfies (LSP). Another interesting class, for which (LSP) holds, consists of those continuous multifunctions $F$ whose values are compact and have convex closure with nonempty interior.
|
Alberto Bressan and Graziano Crasta
|
funct-an math.FA
|
September
| 1,992 |
https://arxiv.org/abs/funct-an/9209001
|
funct-an/9211001
|
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] |
Circle Actions on C*-Algebras, Partial Automorphisms and a Generalized Pimsner-Voiculescu Exact Sequence
|
We introduce a method to study C*-algebras possessing an action of the circle group, from the point of view of its internal structure and its K-theory. Under relatively mild conditions our structure Theorem shows that any C*-algebra, where an action of the circle is given, arises as the result of a construction that generalizes crossed products by the group of integers. Such a generalized crossed product construction is carried out for any partial automorphism of a C*-algebra, where by a partial automorphism we mean an isomorphism between two ideals of the given algebra. Our second main result is an extension to crossed products by partial automorphisms, of the celebrated Pimsner-Voiculescu exact sequence for K-groups. The representation theory of the algebra arising from our construction is shown to parallel the representation theory for C*-dynamical systems. In particular, we generalize several of the main results relating to regular and covariant representations of crossed products.
|
Ruy Exel
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211001
|
funct-an/9211002
|
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] |
C*-algebras and numerical linear algebra
|
We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near points of the essential spectrum of the given operator, and we prove that their averages converge to a measure concentrated precisely on the essential spectrum. In the primary cases of interest, namely the discretized Hamiltonians of one-dimensional quantum systems, this limiting measure is associated with a tracial state on a certain simple C*-algebra. These results have led us to conclude that one must view this kind of numerical analysis in the context of C*-algebras.
|
William Arveson
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211002
|
funct-an/9211003
|
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] |
Improper filtrations for C*-algebras: spectra of unilateral tridiagonal operators
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We extend the results of our previous paper "C*-algebras and numerical linear algebra" to cover the case of "unilateral" sections. This situation bears a close resemblance to the case of Toeplitz operators on Hardy spaces, in spite of the fact that the operators here are far from Toeplitz operators. In particular, there is a short exact sequence 0 --> K --> A --> B --> 0 whose properties are essential to the problem of computing the spectra of self adjoint operators.
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William Arveson
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funct-an math.OA
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November
| 1,992 |
https://arxiv.org/abs/funct-an/9211003
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funct-an/9211004
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] |
Approximately Finite C*-Algebras and Partial Automorphisms
|
We prove that every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism. The case of UHF-algebras is treated in detail.
|
Ruy Exel
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211004
|
funct-an/9211005
|
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] |
A Short Proof that $M_{n}(A)$ is local if $A$ is local and Fr\'echet
|
We give a short and very general proof of the fact that the property of a dense Fr\'echet subalgebra of a Banach algebra being local, or closed under the holomorphic functional calculus in the Banach algebra, is preserved by tensoring with the $n\times n$ matrix algebra of the complex numbers.
|
Larry B. Schweitzer
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211005
|
funct-an/9211006
|
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] |
A Non-Spectral Dense Banach Subalgebra of the Irrational Rotation Algebra
|
We give an example of a dense, simple, unital Banach subalgebra $A$ of the irrational rotation C*-algebra $B$, such that $A$ is not a spectral subalgebra of $B$. This answers a question posed in T.W. Palmer's paper [1].
|
Larry B. Schweitzer
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211006
|
funct-an/9211007
|
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] |
Representable K-theory of Smooth Crossed Products by R and Z
|
We show that the Thom isomorphism and the Pimsner-Voiculescu exact sequence both hold for smooth crossed products of Frechet algebras by R and Z respectively. We also obtain the same results for L^{1}-crossed products of Banach algebras by R and Z.
|
N. Christopher Phillips and Larry B. Schweitzer
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211007
|
funct-an/9211008
|
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] |
An analytic structure emerging in presence of infinitely many odd coordinates
|
This is a contribution to the program of featuring even geometry as a ``collective effect in infinite-dimensional odd geometry,'' as suggested by Manin. We show that the (Gel'fand) spectrum of the locally convex nonstandard hull (in the sense of Luxemburg) of a grassmannian algebra with infinitely many odd generators contains a nontrivial analytic part.
|
Vladimir G. Pestov
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211008
|
funct-an/9211009
|
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] |
Spectral Invariance of Dense Subalgebras of Operator Algebras
|
We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie group, not necessarily connected, then the smooth crossed product G\rtimes A is spectral invariant in the C*-crossed product G\rtimes B. Examples of such groups are given by finitely generated polynomial growth discrete groups, compact or connected nilpotent Lie groups, the group of Euclidean motions on the plane, the Mautner group, or any closed subgroup of one of these. Our theorem gives the spectral invariance of G\rtimes A if A is the set of C^{\infty}-vectors for the action of G on B, or if B= C_{0}(M), and A is a set of G-differentiable Schwartz functions S(M) on M. This gives many examples of spectral invariant dense subalgebras for the C*-algebras associated with dynamical systems. We also obtain relevant results about exact sequences, subalgebras, tensoring by smooth compact operators, and strong spectral invariance in L_{1}(G, B).
|
Larry B. Schweitzer
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211009
|
funct-an/9211010
|
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] |
Dense m-convex Frechet Subalgebras of Operator Algebra Crossed Products by Lie Groups
|
Let A be a dense Frechet *-subalgebra of a C*-algebra B. (We do not require Frechet algebras to be m-convex.) Let G be a Lie group, not necessarily con- nected, which acts on both $A$ and B by *-automorphisms, and let \s be a sub- multiplicative function from G to the nonnegative real numbers. If \s and the action of G on A satisfy certain simple properties, we define a dense Frechet *-subalgebra G\rtimes^{\s} A of the crossed product L^{1}(G, B). Our algebra consists of differentiable A-valued functions on G, rapidly vanishing in \s. We give conditions on the action of G on A which imply the m-convexity of the dense subalgebra G\rtimes^{\s}A. A locally convex algebra is said to be m-con- vex if there is a family of submultiplicative seminorms for the topology of the algebra. The property of m-convexity is important for a Frechet algebra, and is useful in modern operator theory. If G acts as a transformation group on a manifold M, we develop a class of dense subalgebras for the crossed product L^{1}(G, C_{0}(M)), where C_{0}(M) denotes the continuous functions on M vanishing at infinity with the sup norm topology.We define Schwartz functions S(M) on M, which are differentiable with respect to some group action on M, and are rapidly vanishing with respect to some scale on M. We then form a dense m-convex Frechet *-subalgebra G\rtimes^ {\s} S(M) of rapidly vanishing, G-differentiable functions from G to S(M). If the reciprocal of \s is in L^{p}(G) for some p, we prove that our group algebras S^{\s}(G) are nuclear Frechet spaces, and that G\rtimes^{\s}A is the projective completion S^{\s}(G) \otimes A.
|
Larry B. Schweitzer
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211010
|
funct-an/9211011
|
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] |
On certain free product factors via an extended matrix model
|
Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the hyperfinite II$_1$ factor, showing that $$ L(F_n) * R = L(F_(n+1)) $$ for $n \ge 1$, (where $L(F_1)=L(Z)$).
|
Ken Dykema
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211011
|
funct-an/9211012
|
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] |
Interpolated free group factors
|
The interpolated free group factors L(F_r), 1 < r <= \infty, are defined and proofs of their properties with respect to compression by projections and taking free products are proved. Hence it follows that all the free group factor are isomorphic to each other or none of them are. These factors were defined and these properties were proved independently by F. Radulescu, and those given in this paper are equivalent, but use different techniques. Specifically, we develop algebraic techniques that allow us to show that R*R = L(F_2), where R is the hyperfinite II_1 factor.
|
Ken Dykema
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211012
|
funct-an/9211013
|
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] |
Free products of hyperfinite von Neumann algebras and free dimension
|
The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated free group factor $L(\freeF_r)$. The finite dimensional part depends on the minimal projections of the original algebras and the "dimension", r, of the free group factor part is found using the notion of free dimension. For discrete amenable groups $G$ and $H$ this implies that the group von Neumann algebra $L(G*H)$ is an interpolated free group factor and depends only on the orders of $G$ and $H$.
|
Ken Dykema
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211013
|
funct-an/9211014
|
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] |
Non-commutative spheres and numerical quantum mechanics
|
We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
|
William Arveson
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211014
|
funct-an/9211015
|
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] |
Discretized CCR algebras
|
We discuss how the canonical commutation relations must be modified in order to make appropriate numerical models of quantum systems. The C*-algebras associated with the discretized CCRs are the non-commutative spheres of Bratteli, Elliott, Evans and Kishimoto.
|
William Arveson
|
funct-an math.OA
|
November
| 1,992 |
https://arxiv.org/abs/funct-an/9211015
|
funct-an/9212001
|
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] |
The free abelian topological group and the free locally convex space on the unit interval
|
We give a complete description of the topological spaces $X$ such that the free abelian topological group $A(X)$ embeds into the free abelian topological group $A(I)$ of the closed unit interval. In particular, the free abelian topological group $A(X)$ of any finite-dimensional compact metrizable space $X$ embeds into $A(I)$. The situation turns out to be somewhat different for free locally convex spaces. Some results for the spaces of continuous functions with the pointwise topology are also obtained. Proofs are based on the classical Kolmogorov's Superposition Theorem.
|
A.G. Leiderman, S.A. Morris and V.G. Pestov
|
funct-an math.OA
|
December
| 1,992 |
https://arxiv.org/abs/funct-an/9212001
|
funct-an/9212002
|
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] |
On von Neumann algebras which are complemented subspaces of B(H)
|
If there exists a completely bounded projection of B(H) onto a von Neumann algebra M on H, then M is injective. If there exists a bounded projection and M is properly infinite, the same conclusion holds.
|
Erik Christensen and Allan M. Sinclair
|
funct-an math.OA
|
December
| 1,992 |
https://arxiv.org/abs/funct-an/9212002
|
funct-an/9212003
|
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] |
Compression Limit Algebras
|
This paper studies direct limits of full upper triangular matrix algebras with embeddings which are not *-extendible. A representation of the limit algebra is found so that the generated C*-algebra is the C*-envelope. Some examples are described.
|
Alan Hopenwasser, Cecelia Laurie
|
funct-an math.OA
|
December
| 1,992 |
https://arxiv.org/abs/funct-an/9212003
|
funct-an/9212004
|
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] |
The Soft Torus II: A Variational Analysis of Commutator Norms
|
The field of C*-algebras over the interval [0,2] for which the fibers are the Soft Tori is shown to be continuous. This result is applied to show that any pair of non-commuting unitary operators can be perturbed (in a weak sense) in such a way to decrease the commutator norm. Perturbations in norm are also considered and a characterization is given for pairs of unitary operators which are local minimum points for the commutator norm in the finite dimensional case.
|
Ruy Exel
|
funct-an math.OA
|
December
| 1,992 |
https://arxiv.org/abs/funct-an/9212004
|
funct-an/9212005
|
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] |
A Fredholm Operator Approach To Morita Equivalence
|
Given C*-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X_* : K_i(A) --> K_i(B) where K_i denote the complex K-theory functors for i=0, 1. Our techniques do not require separability nor existence of countable approximate identities. We thus extend, to general C*-algebras, the result of Brown, Green and Rieffel according to which strongly Morita equivalent C*-algebras have isomorphic K-groups. The method employed includes a study of Fredholm operators on Hilbert modules.
|
Ruy Exel
|
funct-an math.OA
|
December
| 1,992 |
https://arxiv.org/abs/funct-an/9212005
|
gr-qc/9207001
|
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] |
Non-Minimally Coupled Scalar Field and Ashtekar Variables
|
The non-minimal coupling of a scalar field is considered in the framework of Ashtekar's new variables formulation of gravity. A first order action functional for this system is derived in which the field variables are a tetrad field, and an SL(2,C) connection, together with the scalar field. The tetrad field and the SL(2,C) connection are related to the Ashtekar variables for the vacuum case by a conformal transformation. A canonical analysis shows that for this coupling the equations of Ashtekar's formulation of canonical gravity are non-polynomial in the scalar field. (to be published in Phys. Rev. D)
|
Riccardo Capovilla
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207001
|
gr-qc/9207002
|
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] |
Remarks on Pure Spin Connection Formulations of Gravity
|
In the derivation of a pure spin connection action functional for gravity two methods have been proposed. The first starts from a first order lagrangian formulation, the second from a hamiltonian formulation. In this note we show that they lead to identical results for the specific cases of pure gravity with or without a cosmological constant.
|
Riccardo Capovilla and Ted Jacobson
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207002
|
gr-qc/9207003
|
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] |
Nonsymmetric Gravity Theories: Inconsistencies and a Cure
|
Motivated by the apparent dependence of string $\sigma$--models on the sum of spacetime metric and antisymmetric tensor fields, we reconsider gravity theories constructed from a nonsymmetric metric. We first show that all such "geometrical" theories homogeneous in second derivatives violate standard physical requirements: ghost-freedom, absence of algebraic inconsistencies or continuity of degree-of-freedom content. This no-go result applies in particular to the old unified theory of Einstein and its recent avatars. However, we find that the addition of nonderivative, ``cosmological'' terms formally restores consistency by giving a mass to the antisymmetric tensor field, thereby transmuting it into a fifth-force-like massive vector but with novel possible matter couplings. The resulting macroscopic models also exhibit ``van der Waals''-type gravitational effects, and may provide useful phenomenological foils to general relativity.
|
T. Damour (IHES and DARC) S. Deser (Brandeis University) J. McCarthy (University of Adelaide)
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207003
|
gr-qc/9207004
|
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] |
One Formulation for both Lineal Gravities through a Dimensional Reduction
|
The two lineal gravities --- based on the de Sitter group or a central extension of the Poincar\'e group in 1+1 dimensions --- are shown to derive classically from a unique topological gauge theory. This one is obtained after a dimensional reduction of a Chern--Simons model, which describes pure gravity in 2+1 dimensions, the gauge symmetry being given by an extension of ISO(2,1).
|
Daniel Cangemi
|
gr-qc hep-th
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207004
|
gr-qc/9207005
|
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] |
Degenerate Extensions of General Relativity
|
General relativity has previously been extended to incorporate degenerate metrics using Ashtekar's hamiltonian formulation of the theory. In this letter, we show that a natural alternative choice for the form of the hamiltonian constraints leads to a theory which agrees with GR for non-degenerate metrics, but differs in the degenerate sector from Ashtekar's original degenerate extension. The Poisson bracket algebra of the alternative constraints closes in the non-degenerate sector, with structure functions that involve the {\it inverse} of the spatial triad. Thus, the algebra does {\it not} close in the degenerate sector. We find that it must be supplemented by an infinite number ofsecondary constraints, which are shown to be first class (although their explicit form is not worked out in detail). All of the constraints taken together are implied by, but do not imply, Ashtekar's original form of constraints. Thus, the alternative constraints give rise to a different degenerate extension of GR. In the corresponding quantum theory, the single loop and intersecting loop holonomy states found in the connection representation satisfy {\it all} of the constraints. These states are therefore exact (formal) solutions to this alternative degenerate extension of quantum gravity, even though they are {\it not} solutions to the usual vector constraint.
|
Ted Jacobson and Joseph D. Romano
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207005
|
gr-qc/9207006
|
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] |
The Spin Holonomy Group In General Relativity
|
It has recently been shown by Goldberg et al that the holonomy group of the chiral spin-connection is preserved under time evolution in vacuum general relativity. Here, the underlying reason for the time-independence of the holonomy group is traced to the self-duality of the curvature 2-form for an Einstein space. This observation reveals that the holonomy group is time-independent not only in vacuum, but also in the presence of a cosmological constant. It also shows that once matter is coupled to gravity, the "conservation of holonomy" is lost. When the fundamental group of space is non-trivial, the holonomy group need not be connected. For each homotopy class of loops, the holonomies comprise a coset of the full holonomy group modulo its connected component. These cosets are also time-independent. All possible holonomy groups that can arise are classified, and examples are given of connections with these holonomy groups. The classification of local and global solutions with given holonomy groups is discussed.
|
Ted Jacobson and Joseph D. Romano
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207006
|
gr-qc/9207007
|
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] |
Comments on Theoretical Problems in Nonsymmetric Gravitational Theory
|
Damour, Deser and McCarthy have claimed that the nonsymmetric gravitational theory (NGT) is untenable due to curvature coupled ghost modes and bad asymptotic behavior. This claim is false for it is based on a physically inaccurate treatment of wave propagation on a curved background and an incorrect method for extracting asymptotic behavior. We show that the flux of gravitational radiation in NGT is finite in magnitude and positive in sign.
|
N. J. Cornish and J. W. Moffat
|
gr-qc astro-ph
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207007
|
gr-qc/9207008
|
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] |
The No-Hair Theorem for the Abelian Higgs Model
|
We consider the general procedure for proving no-hair theorems for static, spherically symmetric black holes. We apply this method to the abelian Higgs model and find a proof of the no-hair conjecture that circumvents the objections raised against the original proof due to Adler and Pearson.
|
Amitabha Lahiri
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207008
|
gr-qc/9207009
|
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] |
Gravitational Waves from an Axi-symmetric Source in the Nonsymmetric Grav. Theory
|
We examine gravitational waves in an isolated axi--symmetric reflexion symmetric NGT system. The structure of the vacuum field equations is analyzed and the exact solutions for the field variables in the metric tensor are found in the form of expansions in powers of a radial coordinate. We find that in the NGT axially symmetric case the mass of the system remains constant only if the system is static (as it necessarily is in the case of spherical symmetry). If the system radiates, then the mass decreases monotonically and the energy flux associated with waves is positive.
|
J. W. Moffat and D. C. Tatarski
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207009
|
gr-qc/9207010
|
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0.3636462390422821,
-0.590005099773407
] |
The Dirac Equation Is Separable On The Dyon Black Hole Metric
|
Using the tetrad formalism, we carry out the separation of variables for the massive complex Dirac equation in the gravitational and electromagnetic field of a four-parameter (mass, angular momentum, electric and magnetic charges) black hole.
|
\.Ibrahim Semiz (Yale U.)
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207010
|
gr-qc/9207011
|
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] |
Centrifugal force in Kerr geometry
|
We have obtained the correct expression for the centrifugal force acting on a particle at the equatorial circumference of a rotating body in the locally non-rotating frame of the Kerr geometry. Using this expression for the equilibrium of an element on the surface of a slowly rotating Maclaurin spheroid, we obtain the expression for the ellipticity (as discussed earlier by Abramowicz and Miller) and determine the radius at which the ellipticity is maximum.
|
Sai Iyer and A R Prasanna
|
gr-qc
|
July
| 1,992 |
https://arxiv.org/abs/gr-qc/9207011
|
gr-qc/9208001
|
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] |
The Interpretation of Quantum Cosmological Models
|
We consider the problem of extracting physical predictions from the wave function of the universe in quantum cosmological models. We state the features of quantum cosmology an interpretational scheme should confront. We discuss the Everett interpretation, and extensions of it, and their application to quantum cosmology. We review the steps that are normally taken in the process of extracting predictions from solutions to the Wheeler-DeWitt equation for quantum cosmological models. Some difficulties and their possible resolution are discussed. We conclude that the usual wave function-based approach admits at best a rather heuristic interpretation, although it may in the future be justified by appeal to the decoherent histories approach.
|
Jonathan J. Halliwell
|
gr-qc hep-th
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208001
|
gr-qc/9208002
|
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] |
Thermodynamics of Two-Dimensional Black-Holes
|
We explore the thermodynamics of a general class of two dimensional dilatonic black-holes. A simple prescription is given that allows us to compute the mass, entropy and thermodynamic potentials, with results in agreement with those obtained by other methods, when available.
|
Chiara R. Nappi and Andrea Pasquinucci
|
gr-qc hep-th
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208002
|
gr-qc/9208003
|
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] |
Generation of seed perturbations from Quantum Cosmology
|
The origin of seed perturbations in the Universe is studied within the framework of a specific minisuperspace model. It is shown that the `creation' of the Universe as a result of a quantum transition from a flat empty spacetime would lead to a flat FLRW (Friedmann Lema\^\i tre Robertson-Walker) Universe with weak inhomogeneous perturbations at large wavelengths. The power spectrum of these perturbations is found to be scale invariant at horizon crossing (i.e., the Harrison-Zeldovich spectrum). It is also recognised that the seed perturbations generated in our model would be generically of the isocurvature kind.
|
Tarun Souradeep
|
gr-qc astro-ph
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208003
|
gr-qc/9208004
|
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] |
The $D\to 2$ Limit of General Relativity
|
A method for taking the $D\to 2$ limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy. We show how this theory is related to those obtained via an alternative dimensional reduction approach.
|
R.B. Mann and S.F. Ross
|
gr-qc hep-th
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208004
|
gr-qc/9208005
|
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] |
Nonlinear Noise in Cosmology
|
This paper derives and analyzes exact, nonlocal Langevin equations appropriate in a cosmological setting to describe the interaction of some collective degree of freedom with a surrounding ``environment.'' Formally, these equations are much more general, involving as they do a more or less arbitrary ``system,'' characterized by some time-dependent potential, which is coupled via a nonlinear, time-dependent interaction to a ``bath'' of oscillators with time-dependent frequencies. The analysis reveals that, even in a Markov limit, which can often be justified, the time dependences and nonlinearities can induce new and potentially significant effects, such as systematic and stochastic mass renormalizations and state-dependent ``memory'' functions, aside from the standard ``friction'' of a heuristic Langevin description. One specific example is discussed in detail, namely the case of an inflaton field, characterized by a Landau-Ginsburg potential, that is coupled quadratically to a bath of scalar ``radiation.'' The principal conclusion derived from this example is that nonlinearities and time-dependent couplings do {\em not} preclude the possibility of deriving a fluctuation-dissipation theorem, and do {\em not} change the form of the late-time steady state solution for the system, but {\em can} significantly shorten the time scale for the approach towards the steady state.
|
Salman Habib and Henry E. Kandrup
|
gr-qc
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208005
|
gr-qc/9208006
|
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] |
Stochastic Inflation:The Quantum Phase Space Approach
|
In this paper a quantum mechanical phase space picture is constructed for coarse-grained free quantum fields in an inflationary Universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase space quantum distribution function are found for the cases of power law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field theoretic results (we do not restrict ourselves only to $\VEV{\F^2}$). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse-graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does {\em not} by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence.
|
Salman Habib
|
gr-qc
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208006
|
gr-qc/9208007
|
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] |
There is no $R^3 X S^1$ vacuum gravitational instanton
|
Gravitational instantons, solutions to the euclidean Einstein equations, with topology $R^3 XS^1$ arise naturally in any discussion of finite temperature quantum gravity. This Letter shows that all such instantons (irrespective of their interior behaviour) must have the same asymptotic structure as the Schwarzschild instanton. Using this, it can be shown that if the Ricci tensor of the manifold is non-negative it must be flat. One special case is when the Ricci tensor vanishes; hence one can conclude that there is no nontrivial vacuum gravitational instanton. This result has uses both in quantum and classical gravity. It places a significant restriction on the instabilities of hot flat space. It also can be used to show that any static vacuum Lorentzian Kaluza-Klein solution is flat.
|
Niall \'O Murchadha and Hugh Shanahan
|
gr-qc hep-th
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208007
|
gr-qc/9208008
|
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] |
Trapped surfaces and spherical closed cosmologies
|
This article gives necessary and sufficient conditions for the formation of trapped surfaces in spherically symmetric initial data defined on a closed manifold. Such trapped surfaces surround a region in which there occurs an enhancement of matter over the average. The conditions are posed directly in terms of physical variables and show that what one needs is a relatively large amount of excess matter confined to a small volume. The expansion of the universe and an outward flow of matter oppose the formation of trapped surfaces; an inward flow of matter helps. The model can be regarded as a Friedmann-Lema\^\i tre-Walker cosmology with localized spherical inhomogeneities. We show that the total excess mass cannot be too large.
|
Edward Malec and Niall \'O Murchadha
|
gr-qc astro-ph
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208008
|
gr-qc/9208009
|
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] |
The Entropy of the Gravitational Field
|
We derive a formula for the nonequilibrium entropy of a classical stochastic field in terms of correlation functions of this field. The formalism is then applied to define the entropy of gravitational perturbations (both gravitational waves and density fluctuations). We calculate this entropy in a specific cosmological model (the inflationary Universe) and find that on scales of interest in cosmology the entropy in both density perturbations and gravitational waves exceeds the entropy of statistical fluctuations of the microwave background. The nonequilibrium entropy discussed here is a measure of loss of information about the system. We discuss the origin of the entropy in our cosmological models and compare the definition of entropy in terms of correlation functions with the microcanonical definition in quantum statistical mechanics.
|
R. Brandenberger(Brown), T.Prokopec(Brown), V. Mukhanov(ETH, Zurich)
|
gr-qc astro-ph hep-th
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208009
|
gr-qc/9208010
|
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] |
Massive Analogue of Ashtekar-CJD Action
|
The action of Ashtekar gravity have been found by Cappovilla, Jacobson and Dell. It does not depend on the metric nor the signature of the space-time. The action has a similar structure as that of a massless relativistic particle. The former is naturally generalized by adding a term analogous to a mass term of the relativistic particle. The new action possesses a constant parameter regarded as a kind of a cosmological constant. It is interesting to find a covariant Einstein equation from the action. In order to do it we will examine how the geometrical quantities are determined from the non-metric action and how the Einstein equation follows from it.
|
K.Kamimura and T.Fukuyama
|
gr-qc hep-th
|
August
| 1,992 |
https://arxiv.org/abs/gr-qc/9208010
|
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