Related papers: Superluminal problem in diffusion of relativistic …
Superluminal propagation is an intrinsic problem in the diffusion equation and has not been effectively addressed for a long time. In this work, a rigorous solution to this issue is obtained under the assumption that particles undergo a…
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…
The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on…
We solve a physically significant extension of a classic problem in the theory of diffusion, namely the Ornstein-Uhlenbeck process [G. E. Ornstein and L. S. Uhlenbeck, Phys. Rev. 36, 823, (1930)]. Our generalised Ornstein-Uhlenbeck systems…
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…
This paper summarizes recent developments in the study of the propagation of ultra-high energy cosmic ray protons or nuclei in the Universe, with emphasis on the consequences of energy losses and on the influence of extra-galactic magnetic…
We present a detailed analytical study of the propagation of ultra high energy (UHE) particles in extragalactic magnetic fields. The crucial parameter which affects the diffuse spectrum is the separation between sources. In the case of a…
In this work we simulate the propagation of Ultra High Energy (UHE) protons in the magnetised intergalactic medium of Galaxy Clusters (GCs). Differently from previous works on the subject, we trace proton trajectories in configurations of…
Motivated by a number of recent experiments, we discuss in this paper a speculative but physically admissible form and solutions of effective Maxwell-like equations describing propagation of electromagnetic field in a medium which ``feels''…
We discuss the problem of ultra high energy nuclei propagation in astrophysical backgrounds. We present a new analytical computation scheme based on the hypothesis of continuos energy losses in a kinetic formulation of the particles…
In this paper, the expression of the relativistic Maxwell-J\"uttner velocity distribution was deduced in a detailed and didactic way. This distribution was compared with the well-known Maxwell-Boltzmann distribution, which does not take…
By using geometric methods and superenergy tensors, we find new simple criteria for the causal propagation of physical fields in spacetimes of any dimension. The method can be applied easily to many different theories and to arbitrary…
A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions…
We present an analytic solution to diffusion equation for high energy cosmic rays in the expanding universe. The particles are assumed to be ultra-relativistic and they can have energy losses arbitrarily dependent on energy and time. The…
The significance of the Lorentz gauge as a constraint on solutions of Maxwellian waves is discussed. It is proved that recent claims of superluminal propagation of electromagnetic waves rely on an erroneous basis.
The extremely high precision of current astronomical observations demands a much better theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of isolated…
A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian…
We obtain the Maxwell-J\"uttner distribution function at first order in the post-Newtonian approximation within the framework of general relativity. Taking into account the aforesaid distribution function, we compute the particle four-flow…
We use a kinetic-equation approach to describe the propagation of ultra high energy cosmic ray protons and nuclei comparing theoretical results with the observations of the Pierre Auger Observatory.
Recently, a number of experimental observations on the superluminal group velocities of pulses propagating in dispersive media have led to reconsidering electromagnetism theory in an unconventional framework. To consider faster-than-light…