Smilansky-Solomyak model with a ${\delta }^{\prime }$-interaction

Abstract

We investigate a strongly singular version of the model of irreversible dynamics proposed by Smilansky and Solomyak in which the interaction responsible for an abrupt change of the spectrum is of ${\delta }^{\prime }$ type. We determine the spectrum in both the subcritical and supercritical regimes and discuss its character as well as its asymptotic properties of the discrete spectrum in terms of the coupling constant.

arXiv comment11 pages, no figures; minor improvements in version 2, to appear in Phys. Lett. A

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