Related papers: Relativistic diffusion
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 consider overdamped Langevin diffusions in Euclidean space, with curvature equal to the spectral gap. This includes the Ornstein-Uhlenbeck process as well as non-Gaussian and non-product extensions with convex interaction, such as the…
Experimental particle spectra can be successfully described by power-law tailed energy distributions characteristic to canonical equilibrium distributions associated to R\'enyi's or Tsallis' entropy formula - over a wide range of energies,…
A relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time towards a thermal equilibrium limit, is derived from nonequilibrium-statistical considerations: Adapting an…
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…
Energy diffusion due to spontaneous localization (SL) for a relativistically-fast moving particle is examined. SL is an alternative to standard quantum theory in which quantum state reduction is treated as a random physical process which is…
Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuation-dissipation relation easily gets modified and the mobility matrix is no…
Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time…
We discuss general positivity conditions necessary for a definition of a relativistic diffusion on the phase space. We show that Lorentz covariant random vector fields on the forward cone $p^{2}\geq 0$ lead to a definition of a generator of…
We study the Langevin dynamics of a dipole diffusing in a random electrical field E derived from a quenched Gaussian potential. We show that in a suitable adiabatic limit (where the dynamics of the dipole moment is much faster than the…
In this work the explicit solution of the electronic plasma diffusion with radiation reaction force, under the action of an exponential decay external electric field is given. The electron dynamics is described by a classical generalized…
We revisit the double adiabatic evolution equations and extend them to the relativistic and ultrarelativistic regimes. We analytically solve the relativistic, time-dependent drift kinetic equation for a homogeneous, magnetized,…
We consider a class of time-homogeneous diffusion processes on $\mathbb{R}^{n}$ with common invariant measure but varying volatility matrices. In Euclidean space, we show via stochastic control of the diffusion coefficient that the…
We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…
Diffusion of electrons in a two-dimensional system in static random magnetic fields is studied by solving the time-dependent Schr\"{o}dinger equation numerically. The asymptotic behaviors of the second moment of the wave packets and the…
Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
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…