Pavel Exner, Vladimir Lotoreichik, Milos Tater
Spectral and resonance properties of Smilansky Hamiltonian
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ABSTRACT.  We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically. Furthermore, we show that the model has a rich resonance structure.