Chapter

Disorder and interference: localization phenomena

Cord A. Müller and Dominique Delande

in Ultracold Gases and Quantum Information

Published in print May 2011 | ISBN: 9780199603657
Published online September 2011 | e-ISBN: 9780191729515 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199603657.003.0009

Series: Lecture Notes of the Les Houches Summer School

Disorder and interference: localization phenomena

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In the presence of disorder, classical transport is usually diffusive. This chapter deals with the effect of interference between multiply scattered waves on transport properties. Interference may lead to reduced diffusive transport—this is known as weak localization—or to complete inhibition of transport—which is known as Anderson localization or strong localization. Key parameters are the dimension of the system and the strength of the disorder. After introductory sections on a transfer-matrix description of 1D transport, scaling theory of localization, and key numerical and experimental results, a general microscopic theory of transport in disordered systems is presented, with emphasis on experimental realizations with cold atomic gases. Simple examples are the propagation of light in a disordered medium, for which we show results from a live coherent backscattering expriment, and the propagation of atomic matter waves in an effective disordered potential created by an optical speckle. Finally, the dynamical localization transition of the kicked rotor, as observed with cold atoms, is discussed.

Keywords: Anderson localization; strong localization; quantum transport; disordered systems; weak localization; coherent backscattering; scaling theory of localization; kicked rotor; transfer matrix

Chapter.  40129 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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