Anderson Localization for a Multi-Particle Quantum Graph

Abstract

We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis we prove exponential and strong dynamical localization of any order in the Hilbert-Schmidt norm near the spectral edge. Apart from the results on multi-particle systems, we also prove Lifshitz-type asymptotics for single-particle systems. This shows in particular that localization for single-particle quantum graphs holds under a weaker assumption on the random potential than previously known.

40 pages. The presentation has been improved and a couple of corrections have been made

References in corpus (7)

• Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
• Wegner bounds for a two-particle tight binding model
• The bootstrap multiscale analysis for the multi-particle Anderson model
• Quantum graphs with singular two-particle interactions
• Localization on quantum graphs with random edge lengths
• Localization on quantum graphs with random vertex couplings
• A linear Wegner estimate for alloy type Schroedinger operators on metric graphs