The generalized Langevin equation revisited: Analytical expressions for the persistence dynamics of a viscous fluid under a time dependent external force

TL;DR

This paper derives analytical solutions for the generalized Langevin equation with a time-dependent external force, enabling detailed analysis of particle persistence in viscous fluids with validation against molecular dynamics simulations.

Contribution

It provides closed-form solutions for the non--static generalized Langevin and Fokker--Planck equations under time-dependent forces, advancing understanding of non-Markovian particle dynamics.

Findings

Analytical expressions for particle position under time-dependent forces.

Validation of theoretical results with molecular dynamics simulations.

Insights into persistence times within absorbing barriers.

Abstract

The non--static generalized Langevin equation and its corresponding Fokker--Planck equation for the position of a viscous fluid particle were solved in closed form for a time dependent external force. Its solution for a constant external force was obtained analytically. The non--Markovian stochastic differential equation, associated to the dynamics of the position under a colored noise, was then applied to the description of the dynamics and persistence time of particles constrained within absorbing barriers. Comparisons with molecular dynamics were very satisfactory.