Generalized Langevin Equation with Hydrodynamic Backflow: Equilibrium Properties

TL;DR

This paper reviews the equilibrium dynamics of a particle in a visco-elastic medium with hydrodynamic backflow, deriving noise correlations consistent with fluctuation-dissipation, and discusses implications for single-particle tracking.

Contribution

It provides a generalized Langevin equation framework incorporating hydrodynamic effects and derives explicit thermal noise correlations applicable to various external forces.

Findings

Derived explicit thermal noise correlation function.

Unified treatment for particles under different external potentials.

Discussed implications for single-particle tracking experiments.

Abstract

We review equilibrium properties for the dynamics of a single particle evolving in a visco--elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuation-dissipation theorem. We rely on general time-reversal arguments that apply irrespective of the external potential acting on the particle, but also allow one to retrieve existing results derived for free particles and particles in a harmonic trap. Some consequences for the analysis and interpretation of single-particle tracking experiments are briefly discussed.