Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum-tunneling transitions and exact statistical mechanics of
  bistable systems with parametrized Dikand\'e-Kofan\'e double-well potentials   We consider a one-dimensional system of interacting particles, in which
particles are subjected to a bistable potential the double-well shape of which
is tunable via a shape deformability parameter. Our objective is to examine the
impact of shape deformability on the order of transition in quantum tunneling
in the bistable system, and on the possible existence of exact solutions to the
transfer-integral operator associated with the partition function of the
system. The bistable potential is represented by a class composed of three
families of parametrized double-well potentials, whose minima and barrier
height can be tuned distinctly. It is found that the extra degree of freedom,
introduced by the shape deformability parameter, favors a first-order
transition in quantum tunneling, in addition to the second-order transition
predicted with the $\phi^4$ model. This first-order transition in quantum
tunneling, which is consistent with Chudnovsky's conjecture of the influence of
the shape of the potential barrier on the order of thermally-assisted
transitions in bistable systems, is shown to occur at a critical value of the
shape-deformability parameter which is the same for the three families of
parametrized double-well potentials. Concerning the statistical mechanics of
the system, the associate partition function is mapped onto a spectral problem
by means of the transfer-integral formalism. The condition that the partition
function can be exactly integrable, is determined by a criterion enabling exact
eigenvalues and eigenfunctions for the transfer-integral operator. Analytical
expressions of some of these exact eigenvalues and eigenfunctions are given,
and the corresponding ground-state wavefunctions are used to compute the
probability density which is relevant for calculations of thermodynamic
quantities such as the correlation functions and the correlation lengths.

11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys