Relativistic diffusion

Abstract

We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form.We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution.We discuss drag terms leading to an equilibrium distribution.The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Juettner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.

9 pages,some numerical factors corrected

References in corpus (16)

• Transverse momentum and collision energy dependence of high $p_T$ hadron suppression in Au+Au collisions at ultrarelativistic energies
• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Dynamical foundations of nonextensive statistical mechanics
• The Quark-Gluon Plasma: Collective Dynamics and Hard Thermal Loops
• Heavy-Quark Probes of the Quark-Gluon Plasma at RHIC
• Relativistic Corrections to the Sunyaev-Zel'dovich Effect for Clusters of Galaxies
• Transverse Momentum Spectra in Au+Au and d+Au Collisions at $\sqrt{s_{NN}}$=200 GeV and the Pseudorapidity Dependence of High p${}_T$ Suppression
• Classical Transport Theory and Hard Thermal Loops in the Quark-Gluon Plasma
• Non-extensive statistical mechanics and particle spectra in elementary interactions
• Equilibrium Distribution of Heavy Quarks in Fokker-Planck Dynamics
• Deriving the Hard Thermal Loops of QCD from Classical Transport Theory
• Thermal equilibrium and statistical thermometers in special relativity
• Theory of Relativistic Brownian Motion: The (1+3)-Dimensional Case
• Relativistic diffusion processes and random walk models
• Anomalous diffusion of pions at RHIC
• Generalization of Boltzmann Equilibration Dynamics

Cited by in corpus (23)

• A kinetic theory of diffusion in general relativity with cosmological scalar field
• Dynamics of the diffusive DM-DE interaction--dynamical system approach
• Diffusion in the general theory of relativity
• Nonextensive effects on the phase structure of QHD
• Relativistic diffusion with friction on a pseudoriemannian manifold
• Does the diffusion DM-DE interaction model solve cosmological puzzles?
• Energy and entropy of relativistic diffusing particles
• Evolution of a Simple Inhomogeneous Anisotropic Cosmological Model with Diffusion
• Einstein gravity of a diffusing fluid
• Trends to equilibrium for a class of relativistic diffusions
• Relativistic diffusion of elementary particles with spin
• Non-linear relativistic diffusions
• Thermodynamics of diffusive DM/DE systems
• Formulation of the relativistic heat equation and the relativistic kinetic Fokker-Planck equation using GENERIC
• Brownian motion at the speed of light: a Lorentz invariant family of processes
• Dynamics of tilted Bianchi models of types III, IV, V in presence of diffusion
• A relation between diffusion,temperature and the cosmological constant
• Relativistic diffusive motion in thermal electromagnetic fields
• Linearized Kompaneetz equation as a relativistic diffusion
• Relativistic diffusive motion in random electromagnetic fields
• Relativistic diffusion in random gluon fields
• Apparent superluminal velocities and random walk in the velocity space
• Temperature fluctuations in an inhomogeneous diffusive fluid