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Anderson localization from classical trajectories

Piet W. Brouwer and Alexander Altland
Phys. Rev. B 78, 075304 – Published 5 August 2008

Abstract

We show that Anderson localization in quasi-one-dimensional conductors with ballistic electron dynamics, such as an array of ballistic chaotic cavities connected via ballistic contacts, can be understood in terms of classical electron trajectories only. At large length scales, an exponential proliferation of trajectories of nearly identical classical action generates an abundance of interference terms, which eventually leads to a suppression of transport coefficients. We quantitatively describe this mechanism in two different ways: the explicit description of transition probabilities in terms of interfering trajectories, and an hierarchical integration over fluctuations in the classical phase space of the array cavities.

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  • Received 7 February 2008

DOI:https://doi.org/10.1103/PhysRevB.78.075304

©2008 American Physical Society

Authors & Affiliations

Piet W. Brouwer

  • Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

Alexander Altland

  • Institut für Theoretische Physik, Zülpicher Strasse 77, 50937 Köln, Germany

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Issue

Vol. 78, Iss. 7 — 15 August 2008

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