External potential modifies memory of solute particles: A particle-viscous bath model

• Published in: Journal of molecular liquids 2022-01, Vol.346, p.117918, Article 117918
• Main Authors: Tóthová, Jana, Lisý, Vladimír
• Format: Article
• Language: English
• Subjects: Bath response to external field; Brownian motion; External harmonic field; Generalized Langevin equation; Particle-bath model; Viscous bath
• ISSN: 0167-7322
• DOI: 10.1016/j.molliq.2021.117918

The figures show the time dependence of the memory function of a solute and the Laplace-transformed solvent force correlation function. These functions are affected by external harmonic potentials. The blue lines correspond to the smallest stiffness of the potential and the brown lines to the largest one. In the absence of external forces, the correlation time of the thermal force is τ. Small values of s should determine the friction coefficient of the solute. [Display omitted] •The Brownian motion of a solute in a viscous bath of other particles is studied.•The particle-bath model is developed and a new generalized Langevin equation is derived.•All particles in the solution respond to an external harmonic potential.•The memory kernel and thermal force are affected by the external force.•Expressions for the solvent force and solute velocity correlation function are found. The response to external forces is one of the important properties of stochastic processes. In the present paper, we derive the generalized Langevin equation (GLE) for the description of the non-Markovian Brownian motion (BM) of a particle, e.g. a molecular solute in a solvent, in a harmonic potential. It is assumed that not only the solute particle but also the surrounding molecules respond to the external field. This effect is taken into account by a modification of the Caldeira-Legget particle-bath model. It is also assumed that the bath particles experience friction, modeled by the Stokes force. We show that under the influence of the external force the memory function and the random thermal force are affected by the external potential. Explicit expressions for these functions and the elastic force acting on the Brownian particle are obtained in the discrete variant of the model and its continuum approximation. In the latter case, analytical formulas for relevant time correlation functions describing the dynamics of the solute are obtained coming from the memory function that describes its free BM.