A diffusion limit for a test particle in a random distribution of scatterers

Abstract

We consider a point particle moving in a random distribution of obstacles described by a potential barrier. We show that, in a weak-coupling regime, under a diffusion limit suggested by the potential itself, the probability distribution of the particle converges to the solution of the heat equation. The diffusion coefficient is given by the Green-Kubo formula associated to the generator of the diffusion process dictated by the linear Landau equation.

References in corpus (1)

• Lecture Notes on Quantum Brownian Motion

Cited by in corpus (10)

• Derivation of the Fick's Law for the Lorentz Model in a low density regime
• On the theory of Lorentz gases with long range interactions
• From a non-Markovian system to the Landau equation
• Derivation of the linear Landau equation and linear Boltzmann equation from the Lorentz model with magnetic field
• On the growth of a particle coalescing in a Poisson distribution of obstacles
• Kinetic description of a Rayleigh Gas with annihilation
• Diffusive limit for the random Lorentz gas
• Motion among random obstacles on a hyperbolic space
• Kinetic Theory for the Low-Density Lorentz Gas
• Fick's Law for the Lorentz Model in a weak coupling regime