Seminari del Dipartimento
Fisica Matematica Autonomous evolution of electron speeds in a thermostatted
system: exact results Federico Bonetto 18-12-2018 - 15:30 Largo San Leonardo Murialdo,1 - Pal.C - Aula 311 - III piano
We investigate a dynamical system consisting of N particles moving on a d-dimensional torus under the action of an electric field E with a Gaussian thermostat to keep the total energy constant. The particles are also subject to tochastic collisions which randomize direction but do not change the speed. We prove that in the van Hove scaling limit, E -> 0 and t -> t/E^2, the trajectory of the speeds v_i is described by a stochastic differential equation corresponding to diffusion on a constant energy sphere. Our results are based on splitting the system's evolution into a "slow" process and an independent "noise". We show that the noise, suitably rescaled, converges to a Brownian motion.Then we employ the Ito-Lyons continuity theorem to identify the limit of the slow process. |