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.

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

References in corpus (4)

• Schrödinger operators with δ- and δ'-interactions on Lipschitz surfaces and chromatic numbers of associated partitions
• A regular version of Smilansky model
• A magnetic version of the Smilansky-Solomyak model
• Spectral and resonance properties of Smilansky Hamiltonian