Smilansky's model of irreversible quantum graphs, II: the point spectrum

Research paper by W. D. Evans, M. Solomyak

Indexed on: 18 May '05Published on: 18 May '05Published in: Mathematics - Spectral Theory


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.