Related papers: A random flight process associated to a Lorentz ga…
We show that the time evolution of a quantum wavepacket in a periodic potential converges in a combined high-frequency/Boltzmann-Grad limit, up to second order in the coupling constant, to terms that are compatible with the linear Boltzmann…
In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction…
We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…
We study the processes of particle acceleration which take place in the field of a rotating black hole as part of a mechanism of formation of galactic jets within the first parsec from the central source, where gravitation is supposed to be…
An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as…
We consider transport in two billiard models, the infinite horizon Lorentz gas and the stadium channel, presenting analytical results for the spreading packet of particles. We first obtain the cumulative distribution function of traveling…
The effect of random shooting of particles is considered on the basis of solution of the Schrodinger equation and in terms of the Wigner function. Two-particles description shows, in particular, that initial correlation leads to high…
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is…
The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach…
We analyse the large time behaviour of the rate function that describes the probability of large fluctuations of an underlying microscopic model associated to the homogeneous Boltzmann equation, such as the Kac walk. We consider in…
We study the periodic Lorentz gas in the Boltzmann-Grad limit, whose convergence was rigorously established in the seminal work of Marklof-Str\"ombergsson. Extending the two dimensional results of Boca-Zaharescu to higher dimensions, we…
We recently introduced a new family of processes which describe particles which only can move at the speed of light c in the ordinary 3D physical space. The velocity, which randomly changes direction, can be represented as a point on the…
Geometry of relativistic jets in active galaxies provides important information about mechanisms of launching, collimation and acceleration of plasma flow. We propose a new method to probe a boundary shape of a jet on parsec scales -- in…
The transport phenomena of a nonequilibrium lattice gas system are investigated. We consider a simple system that consists of two particles interacting repulsively and the potential forces acting on these particles. Under an external…
We consider a classical system of point particles interacting by means of a short range potential. We prove that, in the low--density (Boltzmann--Grad) limit, the system behaves, for short times, as predicted by the associated Boltzmann…
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 demonstrate the possibility of a turbulent flow of electrons in graphene in the hydrodynamic region, by calculating the corresponding turbulent probability density function. This is used to calculate the contribution of the turbulent…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about…