Electrical current in Sinai billiards under general small forces

TL;DR

This paper studies how small external forces influence electrical current in Sinai billiards, providing conditions for reversibility, estimates of current, and characterizations of non-equilibrium steady states.

Contribution

It offers new characterizations of time-reversibility and steady states in Sinai billiards under small forces, with estimates of the resulting electrical current.

Findings

Conditions for time-reversibility under external forces

Estimate of electrical current generated

Characterizations of non-equilibrium steady states

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 an ionized medal. 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.