### Abstract

© 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 |
---|---|

Pages (from-to) | 1128-1147 |

Number of pages | 20 |

Journal | Physica A: Statistical Mechanics and its Applications |

DOIs | |

State | Published - 15 Nov 2016 |

## Fingerprint Dive into the research topics of 'Non-Markovian Brownian motion in a magnetic field and time-dependent force fields'. Together they form a unique fingerprint.

## Cite this

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