Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Matrix Elements and Eigenfunctions in Chaotic Systems   The expected root-mean-square value of a matrix element $A_{\alpha\beta}$ in
a classically chaotic system, where $A$ is a smooth, $\hbar$-independent
function of the coordinates and momenta, and $\alpha$ and $\beta$ label
different energy eigenstates, has been evaluated in the literature in two
different ways: by treating the energy eigenfunctions as gaussian random
variables and averaging $|A_{\alpha\beta}|^2$ over them; and by relating
$|A_{\alpha\beta}|^2$ to the classical time-correlation function of $A$. We
show that these two methods give the same answer only if Berry's formula for
the spatial correlations in the energy eigenfunctions (which is based on a
microcanonical density in phase space) is modified at large separations in a
manner which we previously proposed.

37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex