Spectral and resonance properties of the Smilansky Hamiltonian

•We derive conditions on bound states and on resonances of the Smilansky Hamiltonian.•Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian.•Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.

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 in the subcritical case. Furthermore, we show that the model then has a rich resonance structure.