Pavel Exner and Jiri Lipovsky Smilansky-Solomyak model with a $\delta'$-interaction (254K, pdf) 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 $\delta'$ 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.