Odd Diffusivity of Chiral Random Motion

TL;DR

This paper introduces the concept of odd diffusivity in chiral random motion, deriving Green-Kubo relations and demonstrating its emergence through models and simulations, highlighting a new aspect of anisotropic diffusion in chiral active matter.

Contribution

It derives Green-Kubo relations for odd diffusivity and demonstrates its presence in chiral random walks and molecular dynamics simulations, revealing a novel diffusion property.

Findings

Odd diffusivity is a general feature of chiral random motion.

Green-Kubo relations can quantify odd diffusivity.

Simulations confirm the theoretical predictions.

Abstract

Diffusive transport is characterized by a diffusivity tensor which may, in general, contain both a symmetric and an antisymmetric component. Although the latter is often neglected, we derive Green-Kubo relations showing it to be a general characteristic of random motion breaking time-reversal and parity symmetries, as encountered in chiral active matter. In analogy with the odd viscosity appearing in chiral active fluids, we term this component the odd diffusivity. We show how odd diffusivity emerges in a chiral random walk model, and demonstrate the applicability of the Green-Kubo relations through molecular dynamics simulations of a passive tracer particle diffusing in a chiral active bath.