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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., Comment: 26 pages, 3 figures, IOPLaTeX

Odd-diffusive systems are characterized by transverse responses and exhibit unconventional behaviors in interacting systems. To address the dynamical interparticle rearrangements in a minimal system, we here exactly solve the problem of two hard disk-like interacting odd-diffusing particles. We calculate the probability density function (PDF) of the interacting particles in the Fourier-Laplace domain and find that oddness rotates all modes except the zeroth, resembling a ``mutual rolling'' of interacting odd particles. We show that only the first Fourier mode of the PDF, the polarization, enters the calculation of the force autocorrelation function (FACF) for generic systems with central-force interactions. An analysis of the polarization as a function of time reveals that the relative rotation angle between interacting particles overshoots before relaxation, thereby rationalizing the recently observed oscillating FACF in odd-diffusive systems.

A first-principles approach for active chiral hard disks is presented, that explicitly accounts for steric interactions on the two-body level. We derive an effective one-body equation for the joint probability distribution of ositions and angles of the particles. By projecting onto the angular modes, we write a hierarchy for the lowest hydrodynamic modes, i.e. particle density, polarisation, and nematic tensor. Introducing dimensionless variables in the equations, we highlight the assumptions, which - though inherent - are often included implicit in typical closure schemes of the hierarchy. By considering different regimes of the P{\'e}clet number, the well-known models in active matter can be obtained through our consideration. Explicitly, we derive an effective diffusive description and by going to higher orders in the closure scheme, we show that this first-principles approach results in the recently introduced Active Model B +, a natural extension of the Model B for active processes. Remarkably, here we find that chirality can change the sign of the phenomenological activity parameters.

The force autocorrelation function (FACF), a concept of fundamental interest in statistical mechanics, encodes the effect of interactions on the dynamics of a tagged particle. In equilibrium, the FACF is believed to decay monotonically in time which is a signature of slowing down of the dynamics of the tagged particle due to interactions. Here we analytically show that in odd-diffusive systems, which are characterized by a diffusion tensor with antisymmetric elements, the FACF can become negative and even exhibit temporal oscillations. We also demonstrate that, despite the isotropy, the knowledge of FACF alone is not sufficient to describe the dynamics: the full autocorrelation tensor is required and contains an antisymmetric part. These unusual properties translate into enhanced dynamics of the tagged particle quantified via the self-diffusion coefficient that, remarkably, increases due to particle interactions.

It is generally believed that collisions of particles reduce the self-diffusion coefficient. Here we show that in odd-diffusive systems, which are characterized by diffusion tensors with antisymmetric elements, collisions surprisingly can enhance the self-diffusion. In these systems, due to an inherent curving effect, the motion of particles is facilitated, instead of hindered by collisions leading to a mutual rolling effect. Using a geometric model, we analytically predict the enhancement of the self-diffusion coefficient with increasing density. This counterintuitive behaviour is demonstrated in the archetypal odd-diffusive system of Brownian particles under Lorentz force. We validate our findings by many body Brownian dynamics simulations in dilute systems.

We study the motion of a Brownian particle subjected to Lorentz force due to an external magnetic field. Each spatial degree of freedom of the particle is coupled to a different thermostat. We show that the magnetic field results in correlation between different velocity components in the stationary state. Integrating the velocity autocorrelation matrix, we obtain the diffusion matrix that enters the Fokker-Planck equation for the probability density. The eigenvectors of the diffusion matrix do not align with the temperature axes. As a consequence the Brownian particle performs spatially correlated diffusion. We further show that in the presence of an isotropic confining potential, an unusual, flux-free steady state emerges which is characterized by a non-Boltzmann density distribution, which can be rotated by reversing the magnetic field. The nontrivial steady state properties of our system result from the Lorentz force induced coupling of the spatial degrees of freedom which cease to exist in equilibrium corresponding to a single-temperature system.