Odd diffusion and power-law correlations in chiral mass-transport processes
Abstract
We study mass-conserving Markov jump processes on a square lattice, where masses hop with a preferred rotational sense, thus breaking both time-reversal and mirror symmetries. We consider closed systems with both periodic and open (reflecting) boundaries, the latter supporting a steady-state edge current. We show that odd diffusion, arising from the chiral transport, generically provides a mechanism for the emergence of scale-invariant two-point density correlations in nonequilibrium steady states even in the presence of lattice rotation symmetry -- a mechanism that is qualitatively distinct from the well-known mechanism of anisotropic hopping. We exactly calculate the steady-state equal-time density-density correlations, which exhibit an algebraic decay, C(r) ∼ |r|−4 for |r| ≫ 1. This algebraic behavior results from the interplay between the off-diagonal components of the diffusion and mobility tensors, demonstrating that chiral transport alone can generate power-law correlations in isotropic driven systems. Remarkably, the structure factor in the zero-wavenumber limit and the amplitude of the power laws depend nontrivially on chirality. While increasing chirality initially suppresses large-scale density fluctuations, the fluctuations beyond a threshold odd-diffusion strength vary nonmonotonically with chirality and develop a cusp singularity.
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BibTeX
@misc{das2026diffusion,
title = {{Odd diffusion and power-law correlations in chiral mass-transport processes}},
author = {Koushik Das and Animesh Hazra and Punyabrata Pradhan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16821},
eprint = {2609.16821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16821},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Odd diffusion and power-law correlations in chiral mass-transport processes
AU - Koushik Das
AU - Animesh Hazra
AU - Punyabrata Pradhan
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16821
UR - https://arxiv.org/abs/2609.16821
AB - We study mass-conserving Markov jump processes on a square lattice, where masses hop with a preferred rotational sense, thus breaking both time-reversal and mirror symmetries. We consider closed systems with both periodic and open (reflecting) boundaries, the latter supporting a steady-state edge current. We show that odd diffusion, arising from the chiral transport, generically provides a mechanism for the emergence of scale-invariant two-point density correlations in nonequilibrium steady states even in the presence of lattice rotation symmetry -- a mechanism that is qualitatively distinct from the well-known mechanism of anisotropic hopping. We exactly calculate the steady-state equal-time density-density correlations, which exhibit an algebraic decay, C(r) ∼ |r|^−4 for |r| ≫ 1. This algebraic behavior results from the interplay between the off-diagonal components of the diffusion and mobility tensors, demonstrating that chiral transport alone can generate power-law correlations in isotropic driven systems. Remarkably, the structure factor in the zero-wavenumber limit and the amplitude of the power laws depend nontrivially on chirality. While increasing chirality initially suppresses large-scale density fluctuations, the fluctuations beyond a threshold odd-diffusion strength vary nonmonotonically with chirality and develop a cusp singularity.
ER -