Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum chaos theory and the spectrum of ideal-MHD instabilities in
  toroidal plasmas   In a fully 3-D system such as a stellarator, the toroidal mode number $n$
ceases to be a good quantum number--all $n$s within a given mode family being
coupled. It is found that the discrete spectrum of unstable ideal MHD
(magnetohydrodynamic) instabilities ceases to exist unless MHD is modified
(regularized) by introducing a short-perpendicular-wavelength cutoff. Attempts
to use ray tracing to estimate the regularized MHD spectrum fail due to the
occurrence of chaotic ray trajectories. In quantum chaos theory, strong chaos
in the semiclassical limit leads to eigenvalue statistics the same as those of
a suitable ensemble of random matrices. For instance, the probability
distribution function for the separation between neighboring eigenvalues is as
derived from random matrix theory and goes to zero at zero separation. This
contrasts with the Poissonian distribution found in separable systems, showing
that a signature of quantum chaos is level repulsion. In order to determine
whether eigenvalues of the regularized MHD problem obey the same statistics as
those of the Schr\"odinger equation in both the separable 1-D case and the
chaotic 3-D cases, we have assembled data sets of ideal MHD eigenvalues for a
Suydam-unstable cylindrical (1-D) equilibrium using \emph{Mathematica} and a
Mercier-unstable (3-D) equilibrium using the CAS3D code. In the 1-D case, we
find that the unregularized Suydam-approximation spectrum has an anomalous peak
at zero eigenvalue separation. On the other hand, regularization by restricting
the domain of $\kvec_{\perp}$ recovers the expected Poissonian distribution. In
the 3-D case we find strong evidence of level repulsion within mode families,
but mixing mode families produces Poissonian statistics.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph