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

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.

References in corpus (1)

• Irreversible quantum graphs

Cited by in corpus (9)

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• A regular analogue of the Smilansky model: spectral properties
• Spectral and resonance properties of Smilansky Hamiltonian
• Spectral analysis of a class of Schroedinger operators exhibiting a parameter-dependent spectral transition
• Smilansky-Solomyak model with a ${\delta }^{\prime }$-interaction
• The Kronig-Penney model in a quadratic channel with $\delta$ interactions. II : Scattering approach