Open Access

Pietro Luigi Muzzeddu, Erik Kalz, Andrea Gambassi, Abhinav Sharma, Ralf Metzler

• Odd-diffusive systems, characterised by broken time-reversal and/or parity, have recently been shown to display counterintuitive features such as interaction-enhanced dynamics in the dilute limit. Here we extend the investigation to the high-density limit of an odd tracer embedded in a soft medium described by the Gaussian core model (GCM) using a field-theoretic approach based on the Dean–Kawasaki equation. Our analysis 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 (Ds) anomaly of the GCM. Ordinarily, Ds exhibits a non-monotonic trend with increasing density, approaching but remaining below the interaction-free diffusion, D0, (Ds < D0) so that Ds ↑ D0 at high densities. In contrast, for an odd tracer, self-diffusion is enhanced (Ds > D0) and the GCM anomaly is inverted, displaying Ds ↓ D0 at high densities. The transition between the standard andOdd-diffusive systems, characterised by broken time-reversal and/or parity, have recently been shown to display counterintuitive features such as interaction-enhanced dynamics in the dilute limit. Here we extend the investigation to the high-density limit of an odd tracer embedded in a soft medium described by the Gaussian core model (GCM) using a field-theoretic approach based on the Dean–Kawasaki equation. Our analysis 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 (Ds) anomaly of the GCM. Ordinarily, Ds exhibits a non-monotonic trend with increasing density, approaching but remaining below the interaction-free diffusion, D0, (Ds < D0) so that Ds ↑ D0 at high densities. In contrast, for an odd tracer, self-diffusion is enhanced (Ds > D0) and the GCM anomaly is inverted, displaying Ds ↓ D0 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 (Ds ≈ D0) across all densities. We validate our theoretical predictions with Brownian dynamics simulations, finding strong agreement between the them.…