A regular version of Smilansky model

Abstract

We discuss a modification of Smilansky model in which a singular potential `channel' is replaced by a regular, below unbounded potential which shrinks as it becomes deeper. We demonstrate that, similarly to the original model, such a system exhibits a spectral transition with respect to the coupling constant, and determine the critical value above which a new spectral branch opens. The result is generalized to situations with multiple potential `channels'.

arXiv commentLaTeX, 17 pages

References in corpus (4)

• Irreversible quantum graphs
• Irreversible Behaviour and Collapse of Wave Packets in a Quantum System with Point Interactions
• Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
• Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below

Cited by in corpus (6)

• A magnetic version of the Smilansky-Solomyak model
• Spectral and resonance properties of Smilansky Hamiltonian
• A regular analogue of the Smilansky model: spectral properties
• 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