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Electrical Current in Sinai Billiards Under General Small Forces

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Abstract

The Lorentz gas of \(\mathbb{Z}^{2}\)-periodic scatterers (or the so called Sinai billiards) can be used to model motion of electrons on a metal. We investigate the linear response for the system under various external forces (during both the flight and the collision). We give some characterizations under which the forced system is time-reversible, and derive an estimate of the electrical current generated by the forced system. Moreover, applying Pesin entropy formula and Young dimension formula, we get several characterizations of the non-equilibrium steady state of the forced system.

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Acknowledgement

We are grateful to the referees for numerous suggestions, which improved this paper significantly. N.C. was partially supported by National Science Foundation, grant DMS-1301537. H.-K.Z. was partially supported by National Science Foundation, grant DMS-1151762, and by the French CNRS with a poste d’accueil position at the Center of Theoretical Physics in Luminy. P.Z. was partially supported by NNSF project (11071231).

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, USA

    Nikolai Chernov

  2. Department of Mathematics and Statistics, UMass Amherst, Amherst, MA, 01002, USA

    Hong-Kun Zhang & Pengfei Zhang

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  1. Nikolai Chernov
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  2. Hong-Kun Zhang
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  3. Pengfei Zhang
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Correspondence to Hong-Kun Zhang.

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Chernov, N., Zhang, HK. & Zhang, P. Electrical Current in Sinai Billiards Under General Small Forces. J Stat Phys 153, 1065–1083 (2013). https://doi.org/10.1007/s10955-013-0870-1

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  • DOI: https://doi.org/10.1007/s10955-013-0870-1

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