Related papers: Relativistic diffusion of particles with a continu…
We consider Wong equations for a particle with a continuous mass spectrum in a random Yang-Mills field approximating the quantum field at finite temperature. We show that particle time evolution can be approximated by a relativistic…
The Lorentz gas, a point particle making mirror-like reflections from an extended collection of scatterers, has been a useful model of deterministic diffusion and related statistical properties for over a century. This survey summarises…
It is argued that two-particle collisions of relativistic particles "at a distance", irrespective of their position in the configuration space, generate uniform distribution of particles in Lorentz invariant phase space.
We review some recent results concerning the derivation of the diffusion equation and the validation of Fick's law for the microscopic model given by the random Lorentz Gas. These results are achieved by using a linear kinetic equation as…
We derive a Lorentz invariant distribution of velocities for a relativistic gas. Our derivation is based on three pillars: the special theory of relativity, the central limit theorem and the Lobachevskyian structure of the velocity space of…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
We discuss relativistic dynamics in a random electromagnetic field which can be considered as a high temperature limit of the quantum electromagnetic field in a heat bath (cavity) moving with a uniform velocity w. We derive diffusion…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper…
The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became…
We describe electromagnetic propagation in a relativistic electron gas at finite temperatures and carrier densities. Using quantum electrodynamics at finite temperatures, we obtain electric and magnetic responses and general constitutive…
We discuss transport equations resulting from relativistic diffusions in the proper time. We show that a solution of the transport equation can be obtained from the solution of the diffusion equation by means of an integration over the…
Deterministic diffusion in temporally oscillating convection is studied for particles with finite mass. The particles are assumed to obey a simple dissipative dynamical system and the particle diffusion is induced by the strange attractor.…
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…
We obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium…
A stationary distribution function that describes the entire processes of propagation of relativistic particles, including the transition between the ballistic and diffusion regimes, is obtained. The spacial component of the constructed…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…
We examine numerically and analytically the problem of the relativistic velocity distribution in a 1-dim relativistic gas in thermal equilibrium. Our derivation is based on the special theory of relativity, the central limit theorem and the…