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

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, the topological analogy with quantum systems, widely invoked to explain their robustness, has lacked a concrete discrete realization. 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 signatures of the topologically protected edge states characteristic of the unitary limit (p=1) persist into the dissipative regime (p<1), decaying anomalously slowly compared to bulk excitations. 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, effective description for odd diffusion, offering a powerful toolkit to predict transport in confined geometries and disordered chiral media.

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BibTeX RIS

BibTeX

@article{wojcik2026chiral,
  title = {{The chiral random walk: A quantum-inspired framework for odd diffusion}},
  author = {Jan W\'ojcik and Erik Kalz},
  journal = {New Journal of Physics},
  year = {2026},
  month = oct,
  doi = {10.1088/1367-2630/aeaf77},
  url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeaf77},
  note = {CC BY 4.0},
}

RIS

TY  - JOUR
TI  - The chiral random walk: A quantum-inspired framework for odd diffusion
AU  - Jan W{\'o}jcik
AU  - Erik Kalz
PY  - 2026
DA  - 2026/10/02
JO  - New Journal of Physics
DO  - 10.1088/1367-2630/aeaf77
UR  - https://iopscience.iop.org/article/10.1088/1367-2630/aeaf77
AB  - 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, the topological analogy with quantum systems, widely invoked to explain their robustness, has lacked a concrete discrete realization. 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 signatures of the topologically protected edge states characteristic of the unitary limit (p=1) persist into the dissipative regime (p<1), decaying anomalously slowly compared to bulk excitations. This correspondence allows us to theoretically ground the robustness of edge flows in classical &#xD;chiral systems using the bulk-boundary correspondence of Floquet topological insulators. Our results provide a discrete, effective description for odd diffusion, offering a powerful toolkit to predict transport in confined geometries and disordered chiral media.
SN  - 1367-2630
ER  -

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