Diffusion of active tracers in fluctuating fields

TL;DR

This paper investigates how particles diffuse in fluctuating scalar fields, providing exact and approximate formulas for the diffusion constant in various regimes, with applications to biological membranes and magnetic systems.

Contribution

It introduces exact and perturbative methods to compute particle diffusion constants in dynamical Gaussian fields, considering the coupling between particles and fields.

Findings

Exact diffusion constant in the adiabatic limit

Perturbative diffusion constant in weak coupling regime

A solvable toy model illustrating key dynamics

Abstract

The problem of a particle diffusion in a fluctuating scalar field is studied. In contrast to most studies of advection diffusion in random fields we analyze the case where the particle position is also coupled to the dynamics of the field. Physical realizations of this problem are numerous and range from the diffusion of proteins in fluctuating membranes and the diffusion of localized magnetic fields in spin systems. We present exact results for the diffusion constant of particles diffusing in dynamical Gaussian fields in the adiabatic limit where the field evolution is much faster than the particle diffusion. In addition we compute the diffusion constant perturbatively, in the weak coupling limit where the interaction of the particle with the field is small, using a Kubo-type relation. Finally we construct a simple toy model which can be solved exactly.