Speaker : Prof. Aaron Nung Kwan Yip (Purdue University)
Title : Long Time Behavior of Brownian Motion in Tilted Periodic Potentials
Time : 2017-07-03 (Mon) 15:00 -
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: We will investigate various limits concerning the long time average velocity V of a Brownian particle diffusing on a periodic potential. The prototype model is Langevin dynamics which incorporates inertia (mass) and friction. The key feature of the current work is the consideration of an additional macroscopic tilt, F. The goal is to understand how the average velocity V depends on F. Interesting thresholds for the value of F can be obtained, in particular under the limit of vanishing friction and noise. Using the averaging theory of Freidlin-Wentzel, the current work provides rigorous mathematical justification of some formulas obtained by Risken. An earlier, fundamental result by Tanaka for Brownian particle diffusing on a random (Brownian) potential will also be discussed.