13-70 Diana Barseghyan, Pavel Exner

A regular version of Smilansky model (154K, pdf) Aug 20, 13

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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'.

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