Oscillatory Force Autocorrelations in Equilibrium Odd-Diffusive Systems.

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.

Active chiral molecules in activity gradients.

While the behavior of active colloidal molecules is well studied now for constant activity, the effect of activity gradients is much less understood. Here, we explore one of the simplest molecules in activity gradients, namely active chiral dimers composed of two particles with opposite active torques of the same magnitude. We show analytically that with increasing torque, the dimer switches its behavior from antichemotactic to chemotactic. The origin of the emergent chemotaxis is the cooperative exploration of an activity gradient by the two particles. While one of the particles moves into higher activity regions, the other moves towards lower activity regions, resulting in a net bias in the direction of higher activity. We do a comparative study of chiral active particles with charged Brownian particles under a magnetic field and show that despite the fundamental similarity in terms of their odd-diffusive behavior, their dynamics and chemotactic behavior are generally not equivalent. We demonstrate this explicitly in a dimer composed of oppositely charged active particles, which remains antichemotactic to any magnetic field.

Collisions Enhance Self-Diffusion in Odd-Diffusive Systems.

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 behavior 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.

Effect of anisotropic diffusion on spinodal decomposition.

We study the phase transition dynamics of a fluid system in which the particles diffuse anisotropically in space. The motivation to study such a situation is provided by systems of interacting magnetic colloidal particles subject to the Lorentz force. The Smoluchowski equation for the many-particle probability distribution then acquires an anisotropic diffusion tensor. We show that in comparison to the isotropic case, anisotropic diffusion results in qualitatively different dynamics of spinodal decomposition. Using the method of dynamical density functional theory, we predict that the intermediate-stage decomposition dynamics are slowed down significantly by anisotropy; the coupling between different Fourier modes is strongly reduced. Numerical calculations are performed for a model (Yukawa) fluid that exhibits gas-liquid phase separation.