Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistics of pre-localized states in disordered conductors   The distribution function of local amplitudes of single-particle states in
disordered conductors is calculated on the basis of the supersymmetric
$\sigma$-model approach using a saddle-point solution of its reduced version.
Although the distribution of relatively small amplitudes can be approximated by
the universal Porter-Thomas formulae known from the random matrix theory, the
statistics of large amplitudes is strongly modified by localization effects. In
particular, we find a multifractal behavior of eigenstates in 2D conductors
which follows from the non-integer power-law scaling for the inverse
participation numbers (IPN) with the size of the system. This result is valid
for all fundamental symmetry classes (unitary, orthogonal and symplectic). The
multifractality is due to the existence of pre-localized states which are
characterized by power-law envelopes of wave functions, $|\psi_t(r)|^2\propto
r^{-2\mu}$, $\mu <1$. The pre-localized states in short quasi-1D wires have the
power-law tails $|\psi (x)|^2\propto x^{-2}$, too, although their IPN's
indicate no fractal behavior. The distribution function of the
largest-amplitude fluctuations of wave functions in 2D and 3D conductors has
logarithmically-normal asymptotics.

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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: math-ph