Quasiperiodic surface Maryland models on quantum graphs

Abstract

We study quantum graphs corresponding to isotropic lattices with quasiperiodic coupling constants given by the same expressions as the coefficients of the discrete surface Maryland model. The absolutely continuous and the pure point spectra are described. It is shown that the transition between them is governed by the Hill operator corresponding to the edge potential.

12 pages

References in corpus (7)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Spectra of Schroedinger operators on equilateral quantum graphs
• On the dense point and absolutely continuous spectrum for Hamiltonians with concentric $\delta$ shells
• Approximations by graphs and emergence of global structures
• On the Spectral and Propagation Properties of the Surface Maryland Model

Cited by in corpus (1)

• Absolutely continuous spectrum for Laplacians on radial metric trees and periodicity