Smilansky-Solomyak model with a $\delta'$-interaction
Pavel Exner, Ji\v{r}\'i Lipovsk\'y
TL;DR
This paper studies a highly singular quantum model with a delta-prime interaction, analyzing its spectral properties and asymptotic behavior across different coupling regimes.
Contribution
It introduces a strongly singular version of the Smilansky-Solomyak model with delta-prime interaction and determines its spectrum in various regimes.
Findings
Spectrum characterized in subcritical and supercritical regimes
Asymptotic properties of the discrete spectrum analyzed
Spectral changes linked to coupling constant variations
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 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.
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