Spectral and resonance properties of Smilansky Hamiltonian
  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. 
Pavel Exner, Vladimir Lotoreichik, Milo\v{s} Tater
math-ph math.MP math.SP quant-ph