Absolute continuity of the spectrum for periodically modulated leaky wires in ${\mathbb{R}}^3$

Abstract

We consider a model of leaky quantum wire in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction.

AMSTeX, 22 pages

References in corpus (1)

• Absolute continuity in periodic thin tubes and strongly coupled leaky wires

Cited by in corpus (6)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Leaky Quantum Graphs: A Review
• Spectral theory for Schrödinger operators with $\delta$-interactions supported on curves in ${\mathbb{R}}^3$
• Absence of bound states for waveguides in 2D periodic structures
• Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions
• Mean--field stability for the junction of quasi 1D systems with Coulomb interactions