Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Graphs: A model for Quantum Chaos   We study the statistical properties of the scattering matrix associated with
generic quantum graphs. The scattering matrix is the quantum analogue of the
classical evolution operator on the graph. For the energy-averaged spectral
form factor of the scattering matrix we have recently derived an exact
combinatorial expression. It is based on a sum over families of periodic orbits
which so far could only be performed in special graphs. Here we present a
simple algorithm implementing this summation for any graph. Our results are in
excellent agreement with direct numerical simulations for various graphs.
Moreover we extend our previous notion of an ensemble of graphs by considering
ensemble averages over random boundary conditions imposed at the vertices. We
show numerically that the corresponding form factor follows the predictions of
random-matrix theory when the number of vertices is large---even when all bond
lengths are degenerate. The corresponding combinatorial sum has a structure
similar to the one obtained previously by performing an energy average under
the assumption of incommensurate bond lengths.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat