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Functional Integration and Disordered Systems

  • Gilles Poirot
Part of the NATO ASI Series book series (NSSB, volume 361)

Abstract

Very often disordered systems are self-averaging in the thermodynamic limit. This means that any physical quantity is almost surely equal to its expectation value. But the “disorder” can be seen as a random potential, i.e. a random scalar field, so that computing mean values is a field theory problem. Thus, functional integration techniques can be used in addition to probabilistic ones which usually fail when the disorder is small. Question: Can rigorous functional integration allow to get results in weakly disordered systems? For instance, is it possible to prove that electrons in a metal with few impurities have extended states, completing the proof of a metal-insulator transition in semi-conductors?

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Gilles Poirot
    • 1
  1. 1.Centre de Physique ThéoriqueEcole PolytechniquePalaiseau cedexFrance

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