6 research outputs found
Relativistic diffusion with friction on a pseudoriemannian manifold
We study a relativistic diffusion equation on the Riemannian phase space
defined by Franchi and Le Jan. We discuss stochastic Ito (Langevin)
differential equations (defining the diffusion) as a perturbation by noise of
the geodesic equation. We show that the expectation value of the angular
momentum and the energy grow exponentially fast. We discuss drifts leading to
an equilibrium. It is shown that the diffusion process corresponding to the
Juettner or quantum equilibrium distributions has a bounded expectation value
of angular momentum and energy. The energy and the angular momentum tend
exponentially fast to their equilibrium values. As examples we discuss a
particle in a plane fronted gravitational wave and a particle in de Sitter
universe. It is shown that the relativistic diffusion of momentum in de Sitter
space is the same as the relativistic diffusion on the Minkowski mass-shell
with the temperature proportional to the de Sitter radius.Comment: the version published in CQ