  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.
