Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum

Details Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum

2005-03-23

arxiv.org/abs/math/0503497v1

Mathematics

Spectral Theory

Scientific paper

10.1088/0305-4470/38/21/007

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.

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