Towards a New Proof of Anderson Localization
Robert Brandenberger (McGill University), Walter Craig (McMaster, University)
TL;DR
This paper presents a novel proof of Anderson localization in one dimension, extending classical results to include a periodic background potential using techniques from random matrix theory.
Contribution
It introduces a new proof method for Anderson localization that incorporates a periodic potential background, bridging quantum localization and cosmological noise analysis.
Findings
Proves localization in a periodic potential setting
Extends classical Anderson localization results
Utilizes random matrix theory techniques
Abstract
The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof of this Anderson localization phenomenon in one spatial dimension, extending the classical result to the case of a periodic background potential. The proof makes use of techniques previously developed to study the effects of noise on reheating in inflationary cosmology, employing methods of random matrix theory.
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