Title:
A brownian limit perturbed by a microscopic potential.
Abstract:
This is a joint work with Jeremy Clark. I will discuss a
one-dimensional model for a massive particle interacting with a gas of
light particles and under the influence of a microscopic periodic
potential. Our model is Markovian and is given by a linear Boltzmann
equation. We study the behavior of the momentum of the massive
particle as the ratio of a single reservoir particle to the massive
particle tends to zero. For the usual scaling, the microscopic
potential does not appear in the Brownian limit, and the momentum
converges to the Orstein-Uhlenbeck process. However, for a smaller
scaling, the total drift in momentum converges to a Brownian motion
time-changed by the local time of the Orstein-Uhlenbeck process.