The Dance of Odd-Diffusive Particles: A Fourier Approach

TL;DR

This paper provides an exact Fourier-based solution for two interacting odd-diffusive particles, revealing how their transverse responses cause unique rotational behaviors and oscillations in force autocorrelation functions.

Contribution

It introduces an exact analytical approach to analyze two interacting odd-diffusive particles, highlighting the role of the first Fourier mode in force correlations and explaining observed oscillations.

Findings

Fourier modes are rotated by oddness, except the zeroth mode.

The first Fourier mode, polarization, determines the force autocorrelation.

Relative rotation angle exhibits overshoot before relaxation, causing oscillations.

Abstract

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.