CONDUCTIVITY OF THE SELF-SIMILAR LORENTZ CHANNEL

Author:

BARRA FELIPE12,GILBERT THOMAS3,REYES SEBASTIAN1

Affiliation:

1. Departamento de Física, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile

2. CIMAT, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile

3. Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium

Abstract

The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonously according to their indices. This special geometry induces a drift of particles flowing from the small to the large scales. In this article we further explore the dynamical and statistical properties of this billiard. We derive from the ensemble average of the velocity a conductivity formula previously obtained by invoking the equality between phase-space contraction rate and the phenomenological entropy production rate. This formula is valid close to equilibrium. We also review other transport and ergodic properties of this billiard.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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