Enhanced diffusion of tracer particles in nonreciprocal mixtures

TL;DR

This paper investigates how non-reciprocal interactions in a binary mixture of Brownian particles can significantly enhance tracer particle diffusion, breaking the Einstein relation, with insights from simulations and analytical models.

Contribution

It introduces a comprehensive analysis of diffusion enhancement due to non-reciprocal interactions, combining simulations with two analytical approaches, including a novel two-body description.

Findings

Non-reciprocity increases effective diffusion coefficients.

Diffusion enhancement linked to transient dimer formation.

Breakdown of Einstein relation observed.

Abstract

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with non-reciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, non-reciprocity can significantly increase the effective diffusion coefficient of tracer particles, and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions; (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the non-reciprocal interactions.