The chiral random walk: A quantum-inspired framework for odd diffusion

TL;DR

This paper introduces a lattice model bridging classical diffusion and quantum topological systems, demonstrating persistent topological edge currents in chiral fluids through a tunable random walk framework.

Contribution

It presents a microscopic lattice model for chiral random walks that connects classical diffusion with quantum topological properties, explaining robustness of edge currents.

Findings

Topological protection persists in dissipative regimes.

The model interpolates between diffusive and quantum topological walks.

Provides a microscopic basis for odd diffusion phenomena.

Abstract

Chirality in active and passive fluids gives rise to odd transport properties, most notably the emergence of robust edge currents that defy standard dissipative dynamics. While these phenomena are well-described by continuum hydrodynamics, a microscopic framework connecting them to their topological origins has remained elusive. Here, we present a lattice model for an isotropic chiral random walk that bridges the gap between classical stochastic diffusion and unitary quantum evolution. By equipping the walker with an internal degree of freedom and a tunable chirality parameter, $p$, we interpolate between a standard diffusive random walk and a deterministic, topologically non-trivial quantum walk. We show that the topological protection characteristic of the unitary limit ($p=1$) remarkably persists into the dissipative regime ($p<1$). This correspondence allows us to theoretically ground the robustness of edge flows in classical chiral systems using the bulk-boundary correspondence of Floquet topological insulators. Our results provide a discrete microscopic description for odd diffusion, offering a powerful toolkit to predict transport in confined geometries and disordered chiral media.