Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy-dependent correlations in the $S$-matrix of chaotic systems   The $M$-dimensional unitary matrix $S(E)$, which describes scattering of
waves, is a strongly fluctuating function of the energy for complex systems
such as ballistic cavities, whose geometry induces chaotic ray dynamics. Its
statistical behaviour can be expressed by means of correlation functions of the
kind $\left \langle S_{ij}(E+\epsilon)S^\dag_{pq}(E-\epsilon)\right\rangle$,
which have been much studied within the random matrix approach. In this work,
we consider correlations involving an arbitrary number of matrix elements and
express them as infinite series in $1/M$, whose coefficients are rational
functions of $\epsilon$. From a mathematical point of view, this may be seen as
a generalization of the Weingarten functions of circular ensembles.

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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: funct-an
1
The categories of this paper are: cs