event
Tuesday 18 Oct 2011: Maths seminar - Directed transport in a stochastic layer
Anatoly Neishtadt - Loughborough University
St Johns Room, Kay Building 16:00-17:00
We consider a one-dimensional motion in a space-periodic potential in the presence of a time-periodic external force with zero time average. This is a customary model for the study of the Hamiltonian ratchet phenomenon. We consider the case when the external force depends on time slowly. We show that the averaged over a very large time interval displacement of typical phase points in the stochastic layer is different from 0. Thus the directed (ratchet) transport occurs. We obtain a formula for the averaged velocity of this transport. Results of numerical simulations are in a good agreement with the analytical results. Existence of such a directed transport was discovered earlier by several groups of authors in numerical experiments. However, no analytic formulas for the velocity of this transport (and even for finding its direction) has been known. This is joint work with X.Leoncini and A.Vasiliev.
