Diffusion And Escape Of Brownian Particles From A Metastable Potential

Ballistic diffusion is the limit of the anomalous diffusion of Brownian motion,whose mean square displacement is proportional to the square of the time.Thederivative thermal noise will be got by taking the time derivation of the solution ofnoise equation which is satisfied by OU process and rescaling under meeting therequest of the noise intensity dimension.The frequency spectrum of the noise obtainedbefore is zero when the frequency equals zero,which is just the determinationconditions of inducing ballistic diffusion.In this essay,firstly,the mean escape time is analytically derived in the piecewiseharmonic potential field of Brown particles which are driven by the derivative thermalnoise,compared to that of OU noise,some qualitative differences are found.When thecorrelation time of the derivative thermal noise is large,the average escape time issignificantly less than that of OU noise;The average escape time decreasesmonotonously with increasing ofτ,which is opposite of OU noise situation;Theaverage escape time of the derivative thermal noise whenτand noise intensityγissmall is correspond to OU noise when the noise intensityγis small andτissmaller;The corresponding physical mechanism is discussed by analyzing the noisespectrum and the dynamic characteristics.Secondly, the Kramers rate is explored byMonte Carlo stimulation,which is inspired by the same noise in the cubic metastablepotential field.We also discuss OU noise under the same parameters.The result showthat the potential well width and barrier height affecting the Kramers rate possessqualitative differences with OU noise.Kramers rate increases monotonously when thewell width increases;With the decreasing of barrier height,the Kramers rate deviatesfrom the Arrhenius law earlier. The physical mechanism are also discussed combiningthe characteristics and the dynamical effects of the noise spectrum.