Brownian motion in a bath responding to external electric fields

• Published in: Journal of molecular liquids 2020-11, Vol.317, p.113920, Article 113920
• Main Authors: Tóthová, Jana, Šoltýs, Alojz, Lisý, Vladimír
• Format: Article
• Language: English
• Subjects: External electric fields; Fluctuation-dissipation theorem; Generalized Langevin equation; Particle-bath system response
• ISSN: 0167-7322; 1873-3166
• DOI: 10.1016/j.molliq.2020.113920

The Brownian motion of a charged particle immersed in a medium of charged particles is considered when the system is placed in electric fields. Coming from the Zwanzig-Caldeira-Legget particle-bath model, we modify it so that not only the Brownian particle (BP) but also the bath particles respond to the external fields. The generalized Langevin equation is derived for stationary systems. Arbitrarily time-dependent electric fields do not affect the memory function, the thermal noise force, and the BP velocity correlation function. Despite the effect of the external field on the bath particles, Kubo's second fluctuation-dissipation theorem remains unchanged. A general equation for the mean velocity of the BP, which is affected by the bath particles' response to the electric field, is obtained and solved for the Drude model of the frequency distribution of the bath oscillators. The figures illustrate the effect of constant and sinusoidal electric forces on the mean velocity V(t) of the charged Brownian particle in a bath of other particles. The bath response to the external force affects neither the memory of the system described by the generalized Langevin equation nor the Kubo's fluctuation-dissipation theorem. However, V(t) may substantially depend on whether (red and green lines) or not (blue line) the surroundings feel the external field. [Display omitted] •The Brownian motion of a charged particle in a bath of other particles is studied.•The Brownian particle and bath particles both respond to external electric fields.•Generalized Langevin equation is derived within the Caldeira-Legget theory.•Kubo's fluctuation-dissipation theorem is not modified by the electric field.•The mean velocity of the Brownian particle is affected by the external field.