  We consider a model of Non-Brownian self-propelled particles with
anti-alignment interactions where particles try to avoid each other by
attempting to turn into opposite directions. The particles undergo apparent
Brownian motion, even though the particle's equations are fully deterministic.
We show that the deterministic interactions lead to internal, dynamical noise.
Starting from the N-particle Liouville equation, a kinetic equation for the
one-particle distribution function is obtained. We show that the usual
mean-field assumption of molecular chaos leads to qualitatively wrong
predictions such as an infinite coefficient of self-diffusion. Going beyond
mean-field and applying the refined assumption of ``one-sided molecular
chaos'', we analytically calculate the scattering of particles in the limit of
low density and obtain explicit expressions for the dynamical noise of an
effective one-particle Langevin-equation and the corresponding self-diffusion.
In this calculation, the so-called superposition principle of traditional
kinetic theory was modified to handle a system with non-Hamiltonian dynamics
involving phase-space compression. The predicted theoretical expressions for
the relaxation of hydrodynamic modes and the self-diffusion coefficient are in
excellent, quantitative agreement with agent-based simulations at small density
and small anti-alignment strength. At large particle densities, a given
particle is constantly approached and abandoned by different collision
partners. Modelling this switching of partners by a random telegraph process
and exactly solving a self-consistent integral equation, we obtain explicit
expressions for the noise correlations of the effective one-particle
Langevin-equation. Comparison with agent-based simulation show very good
agreement.
