Adiabatic transport, Kubo formula and Anderson localization in some lattice and continuum models

A. Elgart

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The different explanations of the Quantum Hall Effect rely on the validity of the linear response theory for a system that has infinite extent. We will present recent results on the adiabatic charge transport in this context for two dimensional lattice (joint work with M. Aizenman and J. Schenker) and continuum (joint work with B. Schlein) models of a non-interacting electron gas. It is proved that if the Fermi energy falls in the localization regime then the Hall transport is correctly described by the linear response Kubo formula. The localization condition is set forth by the fractional moment method, which is by now extended also to continuum models (joint work with M. Aizenman, S. Naboko, J. Schenker and G. Stoltz). In the present talk, besides localization criteria, we will discuss some ideas - Nenciu’s asymptotic expansion, generalized space-momentum inequalities, and finite speed of propagation estimates - which enter the proof.

Original languageEnglish
Title of host publicationXIVth International Congress on Mathematical Physics
Subtitle of host publicationLisbon, 28 July - 2 August 2003
PublisherWorld Scientific Publishing Co.
Number of pages8
ISBN (Electronic)9789812704016
ISBN (Print)981256201X, 9789812562012
StatePublished - 1 Jan 2006
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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