Self-diffusion anomalies of an odd tracer in soft-core media

Odd-diffusive systems, characterised by broken time-reversal and/or parity symmetry, have recently been shown to display counterintuitive features such as interaction-enhanced dynamics in the dilute limit. Here we we extend the investigation to the high-density limit of an odd tracer embedded in a soft-Gaussian core medium (GCM) using a field-theoretic approach based on the Dean-Kawasaki equation. Our theory reveals that interactions can enhance the dynamics of an odd tracer even in dense systems. We demonstrate that oddness results in a complete reversal of the well-known self-diffusion (\(D_\mathrm{s}\)) anomaly of the GCM. Ordinarily, \(D_\mathrm{s}\) exhibits a non-monotonic trend with increasing density, approaching but remaining below the interaction-free diffusion, \(D_0\), (\(D_\mathrm{s} < D_0\)) so that \(D_\mathrm{s} \uparrow D_0\) at high densities. In contrast, for an odd tracer, self-diffusion is enhanced (\(D_\mathrm{s}> D_0\)) and the GCM anomaly is inverted, displaying \(D_\mathrm{s} \downarrow D_0\) at high densities. The transition between the standard and reversed GCM anomaly is governed by the tracer's oddness, with a critical oddness value at which the tracer diffuses as a free particle (\(D_\mathrm{s} \approx D_0\)) across all densities. We validate our theoretical predictions with Brownian dynamics simulations, finding strong agreement between the two.