Brownian motion in a bath affected by an external harmonic potential

• Published in: Physics letters. A 2021-04, Vol.395, p.127220, Article 127220
• Main Authors: Tóthová, Jana, Lisý, Vladimír
• Format: Article
• Language: English
• Subjects: Bath response to external field; External harmonic field; Fluctuation–dissipation theorem; Generalized Langevin equation; Particle-bath model
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2021.127220

•Brownian motion in a bath of oscillators in the presence of an external harmonic field is studied.•The Zwanzig-Caldeira-Legget particle-bath model is modified so that the bath particles respond to the external field.•A new form of the generalized Langevin equation is derived.•The second fluctuation-dissipation relation is proved with the memory function affected by the external field.•Explicit expressions for the memory function and apparent elastic constant are obtained. The Brownian motion is studied within a modification of the Zwanzig-Caldeira-Legget model when both the Brownian particle and the surrounding bath particles respond to an external harmonic field. It is shown for the derived generalized Langevin equation that the second fluctuation-dissipation theorem remains valid but, as distinct from the usual consideration, with the thermal random force depending on the strength of the confinement potential. An approximate method to evaluate the memory function, the apparent stiffness of the external potential, and the time correlation functions used in the description of the Brownian motion is proposed and applied for the frequency distribution of the bath oscillators, which in the absence of external forces corresponds to the exponentially decaying memory function.