Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas

We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric field E as well as a Gaussian thermostat wh...

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Bibliographic Details
Published inJournal of statistical physics Vol. 146; no. 6; pp. 1221 - 1243
Main Authors Bonetto, Federico, Chernov, Nikolai, Korepanov, Alexey, Lebowitz, Joel L.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.03.2012
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Thermostat
Billiard
SRB measure
Green-Kubo
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Summary:We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric field E as well as a Gaussian thermostat which keeps the speed | v | constant. We show that despite the singular nature of the SRB measure its projections on the space coordinates are absolutely continuous. We further show that these projections satisfy linear response laws for small E . Some of these projections are computed numerically. We compare these results with those obtained from simple models in which the collisions with the obstacles are replaced by random collisions. Similarities and differences are noted.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-012-0444-7