Smilansky’s Model of Irreversible Quantum Graphs, Ii: the Point Spectrum

@inproceedings{Solomyak2005SmilanskysMO,
  title={Smilansky’s Model of Irreversible Quantum Graphs, Ii: the Point Spectrum},
  author={Michael Solomyak},
  year={2005}
}
In the model suggested by Smilansky [6] 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 [3] in which we started an 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 part of the paper we apply the variational approach to the study of the point spectrum.