11 research outputs found
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 one-dimensional
oscillators attached at several different points in the graph. The present
paper is the first one in which the case 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
Smilansky's model of irreversible quantum graphs, II: the point 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 different points of the graph. This paper is a
continuation of our investigation of the case K>1. For the sake of simplicity
we consider K=2, but our argument applies to the general situation. In this
second paper we apply the variational approach to the study of the point
spectrum.Comment: 18 page