Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smilansky's model of irreversible quantum graphs, I: the absolutely
  continuous spectrum   In the model suggested by Smilansky one studies an operator describing the
interaction between a quantum graph and a system of $K$ one-dimensional
oscillators attached at several different points in the graph. The present
paper is the first one in which the case $K>1$ is investigated. For the sake of
simplicity we consider K=2, but our argument is of a general character. In this
first of two papers on the problem, we describe the absolutely continuous
spectrum. Our approach is based upon scattering theory.

13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn