Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical properties of resonance widths for open Quantum Graphs   We connect quantum compact graphs with infinite leads, and turn them into
scattering systems. We derive an exact expression for the scattering matrix,
and explain how it is related to the spectrum of the corresponding closed
graph. The resulting expressions allow us to get a clear understanding of the
phenomenon of resonance trapping due to over-critical coupling with the leads.
Finally, we analyze the statistical properties of the resonance widths and
compare our results with the predictions of Random Matrix Theory. Deviations
appearing due to the dynamical nature of the system are pointed out and
explained.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
16
The categories of this paper are: stat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph