Vibrational relaxation of a nonlinear brownian oscillator

Abstract

We study stochastic dynamics driven by white and colored noise by means of the Fokker-Planck process. Two methods for solving the Fokker-Planck equation is introduced. The one is the projection operator method and the other is the matrix continued fraction method. In the white noise limit the study of a nonlinear Brownian oscillator using the projection operator method shows that the vibrational relaxation rate is enhanced not only by the friction and temperature, but also by the nonlinear part of the potential, which suggests that there is a coupling between the nonlinearity and randomly fluctuating force. By the matrix continued fraction method we obtain the similar results. In the case of colored noise, changing the correlation time we examine the trend of the relaxation time of the harmonic oscillator in terms of the projection operator method. And then we compare the results with those of the matrix continued fraction method.