Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

Abstract

In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

Mechanism of barrier crossing dynamics in the presence of both time dependent and independent magnetic fields

“…Very recently the Fokker-Planck equation has been proposed in the natural phase space in a simple way for arbitrary frictional memory kernel [53] and additive thermal noise. The Fokker-Planck equation in the phase space also has been derived in a recent Ref.…”

Comment on "Non-Markovian harmonic oscillator across a magnetic field and time dependent force fields"

“…Here it has been shown that a few extra terms appear in the FPE compared to Ref. [1]. Then to reexamine our calculation we started with the relevant Langevin equations of motion [1,2],…”

“…In a recent paper [1], we derived the Fokker-Planck equations using an alternative method for the non-Markovian dynamics for a free particle and the harmonic oscillator, respectively. Then we extend this method for the non-Markovian dynamics in the presence of a magnetic field.…”

“…[1]. Then to reexamine our calculation we started with the relevant Langevin equations of motion [1,2],…”

“…It is to be noted here that the rest of the off diagonal elements of the matrix, A ′ (t) are zero. Now following the procedure as reported in the recent paper [1]…”