Properties of Stationary Nonequilibrium States in the Thermostatted Lorentz Gas I: the One Particle System

Abstract

We study numerically and analytically the properties of the stationary state of a particle moving under the influence of an electric field $\bE$ in a two dimensional periodic Lorentz gas with the energy kept constant by a Gaussian thermostat. Numerically the current appears to be a continuous function of $\bE$ whose derivative varies very irregularly, possibly in a discontinuous manner. We argue for the non differentibility of the current as a function of $\bE$ utilizing a symbolic description of the dynamics based on the discontinuities of the collision map. The decay of correlations and the behavior of the diffusion constant are also investigated.

References in corpus (3)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
• Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems

Cited by in corpus (7)

• Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system
• Synchronization versus stability of the invariant distribution for a class of globally coupled maps
• Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas
• Spatial structure of Sinai-Ruelle-Bowen measures
• Deterministic Diffusion in Periodic Billiard Models
• Speed Distribution of N Particles in the Thermostated Periodic Lorentz Gas with a Field
• Autonomous evolution of electron speeds in a thermostatted system: exact results