Irreversible quantum graphs

Abstract

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a {\it single} harmonic oscillator is coupled to it. This mechanism is shown to imply that the quantum dynamics is irreversible. Moreover, it demonstrates the surprising result that irreversibility can be introduced by a "bath" which consists of a {\it single} harmonic oscillator.

References in corpus (4)

• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Kirchhoff's Rule for Quantum Wires
• Chaotic Scattering on Graphs
• Quantum Graphs: A simple model for Chaotic Scattering

Cited by in corpus (15)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Irreversible Behaviour and Collapse of Wave Packets in a Quantum System with Point Interactions
• A regular version of Smilansky model
• Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
• A magnetic version of the Smilansky-Solomyak model
• Smilansky's model of irreversible quantum graphs, II: the point spectrum
• A regular analogue of the Smilansky model: spectral properties
• Spectral and resonance properties of Smilansky Hamiltonian
• A trace formula for metric graphs with piecewise constant potentials and multi-mode graphs
• Spectral analysis of a class of Schroedinger operators exhibiting a parameter-dependent spectral transition
• Smilansky-Solomyak model with a ${\delta }^{\prime }$-interaction
• On the absolutely continuous spectrum in a model of irreversible quantum graph
• On a family of differential operators with the coupling parameter in the boundary condition
• The Kronig-Penney model in a quadratic channel with $\delta$ interactions. II : Scattering approach
• On the discrete spectrum of a family of differential operators