Odd diffusivity and odd mobility in a system with equilibrium structure*

Odd transport coefficients may generally appear in systems with broken time-reversal and parity symmetry [1,2]. Typical examples are systems that are driven at the level of individual constituents, and thus have stationary state distributions that are not known explicitly. This makes the analysis of these systems challenging. Here we consider a system of  interacting Brownian particles evolving under the influence of forces that have components transverse to energy gradients [3]. The evolution breaks the time-reversal and parity symmetry but its stationary distribution coincides with the equilibrium distribution. We analyze the tracer dynamics and derive expressions for the self-diffusion and mobility coefficients, including their odd components. A mode-coupling approximation predicts that the ratio of the odd diffusion and odd mobility diverges at the dynamic glass transition, which implies an extreme violation of the Einstein relation.

[1] C. Hargus, J.M. Epstein and K.K. Mandadapu, PRL 127, 178001 (2021).

[2] A.R. Poggioli and D.T. Limmer, PRL 130, 158201 (2023).

[3] F. Ghimenti, L. Berthier, G. Szamel and F. van Wijland, arXiv:2307.02840.