Colloquium on July 2, 2012

Boris Altshuler
Columbia University

Anderson Localization – looking forward.

Localization of the eigenfunctions of quantum particles in a random potential was discovered by P.W. Anderson more than 50 years ago. In spite of its respectable maturity and intensive theoretical and experimental studies this field is far from being exhausted. Anderson localization was originally discovered in connection with spin relaxation and charge transport in disordered conductors. Later this phenomenon was observed for light, microwaves, sound, and more recently for cold atoms.
It also became clear that the domain of applicability of this concept is much broader. For example, it provides an adequate framework for discussing the transition between integrable and chaotic behavior in quantum systems. Moreover, it can be extended to various problems in condensed matter physics that involve not only disorder, but also interaction between quantum particles. We will consider manifestation of the Anderson localization in model systems: interacting Bose and Fermi gases and disordered spin models. This will allow us to discuss such phenomena as superconductor-metal-insulator (superfluid-normal fluid-glass) transitions. In particular, we will introduce a new class of finite-temperature phase transitions that can exist even in one-dimensional systems and manifest themselves in transport rather than equilibrium properties. We will also be able to get some insight on some problems in quantum computational complexity.