Related papers: Density-dependent diffusion in the periodic Lorent…
We consider a two-dimensional Lorentz gas with infinite horizon. This paradigmatic model consists of pointlike particles undergoing elastic collisions with fixed scatterers arranged on a periodic lattice. It was rigorously shown that when…
The two-dimensional, periodic Lorentz gas, is the dynamical system corresponding with the free motion of a point particle in a planar system of fixed circular obstacles centered at the vertices of a square lattice in the Euclidian plane.…
We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study…
In this article, we obtain the rates of convergence for superdiffusion in the Boltzmann-Grad limit of the periodic Lorentz gas, which is one of the fundamental models to study diffusions in deterministic systems. In their seminal work,…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
We investigate the diffusive scaling of the Lorentz gas in the presence of an external force of mean-field type. In the weak coupling regime and for diffusive time scales, the test particle's law converges to the probability density…
The expansion of the conductivity in 2-d quantum Lorentz models in terms of the scatterer density n is considered. We show that nonanalyticities in the density expansion due to scattering processes with small and large momentum transfers,…
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…
We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which…
It is well known that, in the Boltzmann-Grad limit, the distribution of the free path length in the Lorentz gas with disordered scatterer configuration has an exponential density. If, on the other hand, the scatterers are located at the…
Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. Particles reside at adsorption sites with different well depths potentials and jump randomly between…
In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensions d $\geq$ 2. Specifically, we consider a microscopic…
The dynamics of a point charged particle which is driven by a uniform external electric field and moves in a medium of elastic scatterers is investigated. Using rudimentary approaches, we reproduce, in one dimension, the known results that…
We present an analysis of diffusion in terms of the spontaneous density fluctuations in a non-thermal two-species fluid modeled by a lattice gas automaton. The power spectrum of the density correlation function is computed with statistical…
We study the dynamics of a particle moving in a square two-dimensional Lorentz lattice-gas. The underlying lattice-gas is occupied by two kinds of rotators, "right-rotator (R)" and "left-rotator (L)" and some of the sites are empty…
We study the dynamics of a point particle in a periodic array of spherical scatterers, and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit).…
The Lorentz gas is a billiard model involving a point particle diffusing deterministically in a periodic array of convex scatterers. In the two dimensional finite horizon case, in which all trajectories involve collisions with the…
We study chaotic behavior and diffusion in the 2D periodic Lorentz gas in the finite-horizon regime. The dynamical observable which we consider is the length of single particle's trajectories, which moves in a triangular array of rigid…
A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point…
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a…