© 2016 Elsevier B.V. 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.
|Original language||American English|
|Number of pages||20|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - 15 Nov 2016|
Hidalgo-Gonzalez, J. C., Jiménez-Aquino, J. I., & Romero-Bastida, M. (2016). Non-Markovian Brownian motion in a magnetic field and time-dependent force fields. Physica A: Statistical Mechanics and its Applications, 1128-1147. https://doi.org/10.1016/j.physa.2016.06.133