Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level Curvature Distribution and the Structure of Eigenfunctions in
  Disordered Systems   The level curvature distribution function is studied both analytically and
numerically for the case of T-breaking perturbations over the orthogonal
ensemble. The leading correction to the shape of the curvature distribution
beyond the random matrix theory is calculated using the nonlinear
supersymmetric sigma-model and compared to numerical simulations on the
Anderson model. It is predicted analytically and confirmed numerically that the
sign of the correction is different for T-breaking perturbations caused by a
constant vector-potential equivalent to a phase twist in the boundary
conditions, and those caused by a random magnetic field. In the former case it
is shown using a nonperturbative approach that quasi-localized states in weakly
disordered systems can cause the curvature distribution to be nonanalytic. In
$2d$ systems the distribution function $P(K)$ has a branching point at K=0 that
is related to the multifractality of the wave functions and thus should be a
generic feature of all critical eigenstates. A relationship between the
branching power and the multifractality exponent $d_{2}$ is suggested. Evidence
of the branch-cut singularity is found in numerical simulations in $2d$ systems
and at the Anderson transition point in $3d$ systems.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph