Brownian Motion of a Nonlinear Oscillator

Abstract

Brownian motion of a nonlinear oscillator which was studied by Bixon and Zwanzig who started with a nonlinear Langevin equation is re-examined from first principles with the use of a model system in which a nonlinear oscillator is embedded in a heat reservoir composed of a simple cubic lattice. Nonlinear theory of fluctuation recently developed by Mori and Fujisaka is used to obtain a non-linear Langevin equation and a linear non-Markoffian kinetic equation with a renormalized friction term. It is shown that this equation has the same form as that derived by Bixon and Zwanzig.