Absolutely Continuous Spectrum for Quantum Trees

Abstract

We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.

48 pages, 2 figures

References in corpus (5)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
• Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs
• Mean quantum percolation
• Quantum ergodicity for the Anderson model on regular graphs