Anderson Localization for a Multi-Particle Quantum Graph

TL;DR

This paper proves exponential and dynamical localization for multi-particle quantum graphs with random potential using multiscale analysis, and establishes Lifshitz asymptotics for single-particle systems, broadening the understanding of localization phenomena.

Contribution

It introduces a multiscale analysis approach to demonstrate localization in multi-particle quantum graphs and weakens the conditions needed for localization in single-particle cases.

Findings

Exponential localization near the spectral edge for multi-particle systems

Strong dynamical localization in the Hilbert-Schmidt norm

Lifshitz-type asymptotics for single-particle quantum graphs

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.