Abstract
The diffusion of relativistic particle in a fluid at equilibrium is investigated through an analytical and numerical study of the Relativistic Ornstein-Uhlenbeck process (ROUP). Contrary to expectations, the ROUP exhibits short-time propagation in physical space and only displays typical diffuse behavior at asymptotic times. The short-time propagation is understood through an analytical computation and the density profile is fitted at all times by a simple Ansatz. A generalization of Fick’s law is finally obtained, in which the diffusion coefficient is replaced by a time-dependent metric. These results connect relativistic diffusion with gravitational horizons and geometrical flows.
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