Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Statistics for Quantum Graphs: Periodic Orbits and
  Combinatorics   We consider the Schroedinger operator on graphs and study the spectral
statistics of a unitary operator which represents the quantum evolution, or a
quantum map on the graph. This operator is the quantum analogue of the
classical evolution operator of the corresponding classical dynamics on the
same graph. We derive a trace formula, which expresses the spectral density of
the quantum operator in terms of periodic orbits on the graph, and show that
one can reduce the computation of the two-point spectral correlation function
to a well defined combinatorial problem. We illustrate this approach by
considering an ensemble of simple graphs. We prove by a direct computation that
the two-point correlation function coincides with the CUE expression for 2x2
matrices. We derive the same result using the periodic orbit approach in its
combinatorial guise. This involves the use of advanced combinatorial techniques
which we explain.

11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex