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, $C(\mathbf{r}) \sim |\mathbf{r}|<sup>{-4}$ for $|\mathbf{r}| \gg 1$. 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.