Thermal relaxation for the Relativistic Ornstein–Uhlenbeck Process

The thermal relaxation of a relativistic particle diffusing in a fluid at equilibrium is investigated through a numerical study of the Relativistic Ornstein–Uhlenbeck Process. The spectrum of the relaxation operator has both a discrete and a continuous component. Both components are fully characterized and the limit between them is given a simple interpretation. Short-time relaxation is addressed separately, and a global effective relaxation time is also computed. The general conclusion is that relativistic effects slow down thermalization.