Spectral and resonance properties of Smilansky Hamiltonian

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.

arXiv comment16 pages

References in corpus (7)

• Open Quantum Systems. An Introduction
• Irreversible quantum graphs
• A regular version of Smilansky model
• Irreversible Behaviour and Collapse of Wave Packets in a Quantum System with Point Interactions
• Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
• Smilansky's model of irreversible quantum graphs, II: the point spectrum
• Spectral analysis of a class of Schroedinger operators exhibiting a parameter-dependent spectral transition

Cited by in corpus (3)

• A magnetic version of the Smilansky-Solomyak model
• Smilansky-Solomyak model with a ${\delta }^{\prime }$-interaction
• The Kronig-Penney model in a quadratic channel with $\delta$ interactions. II : Scattering approach