Regular Article - Theoretical Physics
Towards a new proof of Anderson localization
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
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Published online: 22 February 2012
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.
© Springer-Verlag / Società Italiana di Fisica, 2012