Validity of Kubo’s Fluctuation–dissipation theorem in systems driven by a time-dependent electric field

J.F. García-Camacho, O. Contreras-Vergara, N. Sánchez-Salas, G. Ares de Parga and J.I. Jiménez-Aquino

Physica A: Statistical Mechanics and its Applications, 2025, vol. 674, issue C

Abstract: The purpose of this work is to corroborate the validity of Kubo’s second Fluctuation-Dissipation Theorem (FDT), for non-Markovian systems described by a generalized Langevin equation (GLE). Additionally, the system is under the action of a time-dependent electric field which can influence not only on the tagged Brownian particle but also on the bath particles. Two theoretical methods are used to show that Kubo’s FDT remains unchanged: one relies upon the Velocity Correlation Function (VCF), and the other one is related to Zwanzig model. Once this is done, the velocity probability density is obtained for arbitrary but well-behaved friction memory kernel and time-dependent electric fields. In the particular case of an Ornstein–Uhlenbeck-type friction memory kernel, we explicitly calculate the mean square velocity for three specific electric fields which are compared with the numerical simulation to validate the theoretical results.

Keywords: Fluctuation-Dissipation Theorem; Brownian particle; Generalized Langevin equation; Ornstein–Uhlenbeck-type process; Stochastic differential equations; Velocity probability density (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125003449

DOI: 10.1016/j.physa.2025.130692

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