05-102 W.D.Evans, M.Solomyak

Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum (347K, pdf) Mar 10, 05

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Abstract. 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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