Related papers: Linearized Kompaneetz equation as a relativistic d…
Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and…
We consider reversible diffusions in random environment and prove the Einstein relation for this model. It says that the derivative of the effective velocity under an additional local drift equals the diffusivity of the model without drift.…
Irreversible processes of one-dimensional quantum perfect Lorentz gas is studied on the basis of the fundamental laws of physics in terms of the complex spectral analysis associated with the resonance state of the Liouville-von Neumann…
We discuss the superluminal problem in the diffusion of ultra high energy protons with energy losses taken into account. The phenomenological solution of this problem is found with help of the generalized J\"uttner propagator, originally…
Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions…
We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in…
A proof of the relativistic $H$-theorem by including nonextensive effects is given. As it happens in the nonrelativistic limit, the molecular chaos hypothesis advanced by Boltzmann does not remain valid, and the second law of thermodynamics…
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…
The linear electromagnetic response of a uniform electron gas to a longitudinal electric field is determined, within the self-consistent-field theory, by the linear polarizability and the Lindhard dielectric function. Using the same…
The paper proposes an envelope soliton model of the electron. The soliton propagates within a waveguide which size varies with the potential. The soliton is the solution of the Schroedinger equation with the addition of a nonlinear term…
We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
The propagation of nonlinear and dispersive waves in various materials can be described by the well-known Kadomtsev-Petviashvili (KP) equation, which is a (2+1)-dimensional partial differential equation. In this paper, we show that the KP…
Examination of equilibrium radiation in plasma media shows that the spectral energy distribution of such radiation is different from the Planck equilibrium radiation. Using the approach of quantum electrodynamics the general relation for…
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
We present a new dispersion relation for photons that are nonlinearly interacting with a radiation gas of arbitrary intensity due to photon-photon scattering. It is found that the photon phase velocity decreases with increasing radiation…
The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The…
Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…