Diffusion of a particle quadratically coupled to a thermally fluctuating field

TL;DR

This paper investigates how a Brownian particle quadratically coupled to a fluctuating field diffuses, revealing that active particles slow down and passive particles' diffusion depends on field fluctuation speed, with analytical and numerical validation.

Contribution

It introduces a path-integral approach to compute the effective diffusion coefficient for quadratically coupled particles, extending previous linear coupling models.

Findings

Active particles are always slowed down by the field.

Passive particles slow down in slow fields and accelerate in fast fields.

Numerical simulations agree with analytical predictions.

Abstract

We study the diffusion of a Brownian particle quadratically coupled to a thermally fluctuating field. In the weak coupling limit, a path-integral formulation allows to compute the effective diffusion coefficient in the cases of an active particle, that tends to suppress the field fluctuations, and of a passive particle, that only undergoes the field fluctuations. We show that the behavior is similar to what was previously found for a linear coupling: an active particle is always slowed down, whereas a passive particle is slowed down in a slow field and accelerated in a fast field. Numerical simulations show a good agreement with the analytical calculations. The examples of a membrane protein coupled to the curvature or composition of the membrane are discussed, with focus on the room for anomalous diffusion.