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

TL;DR

This paper analyzes the spatial structure of nonequilibrium stationary states in a 2D periodic Lorentz gas under external electric field and Gaussian thermostat, revealing absolute continuity of projections and linear response behavior.

Contribution

It provides an analytical and numerical study of the spatial structure and response laws of NESS in the Lorentz gas, including comparisons with simplified models.

Findings

Projections of SRB measure are absolutely continuous.

Projections satisfy linear response laws for small electric fields.

Numerical computations of response laws are presented.

Abstract

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 them 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.