Non-Markovian Brownian motion in a magnetic field and time-dependent force fields

作者：Hidalgo Gonzalez J C; Jimenez Aquino J I^*; Romero Bastida M

来源：Physica A: Statistical Mechanics and Its Applications , 2016, 462: 1128-1147.

DOI：10.1016/j.physa.2016.06.133

• Generalized Langevin equation
• Velocity-space generalized Fokker-Planck equation
• Phase-space generalized Fokker-Planck equation

This work focuses on the derivation of the velocity and phase-space generalized Fokker-Planck equations for a Brownian charged particle embedded in a memory thermal bath and under the action of force fields: a constant magnetic field and arbitrary time dependent force fields. To achieve the aforementioned goal we use a Gaussian but non-Markovian generalized Langevin equation with an arbitrary friction memory kernel. In a similar way, the generalized diffusion equation in the zero inertia limit is also derived. Additionally we show, in the absence of the time-dependent external forces, that, if the fluctuation-dissipation relation of the second kind is valid, then the generalized Langevin dynamics associated with the charged particle reaches a stationary state in the large-time limit. The consistency of our theoretical results is also verified when they are compared with those derived in the absence of the force fields and in the Markovian case.

• 出版日期2016-11-15