PHASE CONVECTION AND DISTRIBUTION TAILS IN PERIODICALLY DRIVEN BROWNIAN-MOTION

A study is performed of the effect of time-periodic driving on the statistics of thermalized particles in a many-dimensional potential well. The heat bath is modelled by adding white noise and damping. The unperturbed Hamiltonian is supposed exactly integrable, and the driving of the order ε weak enough, ε ≪ 1, so that the driven Hamiltonian motion can be described in terms of isolated nonlinear resonances. It is shown that, due to the effect of resonances in many-dimensional case, the "relaxed" distribution, established in large times, corresponds to the circulation of closed-loop fluxes in the phase space - a phenomenon called phase convection. Simultaneously, the "tails" of the "relaxed" distribution function, depending on the temperature T as ρ = Z exp(-φ/kT), are exponentially strongly perturbed, i.e. the quantity φ differs from the corresponding one of the Hibbs distribution φ0 = H0 as φ0 - φ ∼ φ0. In terms of thermally activated rate processes, the phenomenon is the exponentially strong speed-up of the escape rate by periodic driving. © 1990.