RayleighRitz Calculation of Effective Potential Far From Equilibrium.pdf

Rayleigh-Ritz Calculation of Effective Potential Far From Equilibrium Francis J. Alexander a and Gregory L. Eyink b a Center for Computational Science 3 Cummington Street Boston University Boston, Massachusetts 02215 b Department of Mathematics University of Arizona Tucson, Arizona, 85721 (February 5, 2008) 6 9 model consists of a unit mass, charged particle in a 1- 9 We demonstrate the utility of a Rayleigh-Ritz scheme re- dimensional cosine potential V (x) = V cos x, damped 1 cently proposed to compute the nonequilibrium effective po- 0 by linear friction with coefficient γ , and driven both by n tential nonperturbatively in a strong noise regime far from an electric force F = qE and by thermal noise of tem- u equilibrium. A simple Kramers model of an ionic conductor J is used to illustrate the efficiency of the method. perature T = γΘ/kB . The dynamics of individual real- 4