Eur. Phys. J. C (2012) 72: 1881
https://doi.org/10.1140/epjc/s10052-012-1881-9

Regular Article - Theoretical Physics

Towards a new proof of Anderson localization

¹ Department of Physics, McGill University, 3600 Rue Université, Montréal, H3A 2T8, Québec, Canada
² Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

^* e-mail: rhb@physics.mcgill.ca

Received: 2 December 2011
Published online: 22 February 2012

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.