Related papers: Long Range Particle Dynamics and the Linear Boltzm…
Parametric resonance can produce particles from oscillating scalar field, where an exponential growth of the particle number density can be developed. While it has been noticed that stimulated decay in Boltzmann equations exhibits similar…
We consider a system of N particles interacting via a short-range smooth potential, in a intermediate regime between the weak-coupling and the low-density. We provide a rigorous derivation of the Linear Landau equation from this particle…
A small tagged particle immersed in a fluid exhibits the Brownian motion and diffuses at the long-time scale. Meanwhile, at the short-time scale, the dynamics of the tagged particle cannot be simply described by the usual generalized…
Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting…
The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the local well-posedness of the Boltzmann equation in bounded domain with the Cercignani-Lampis boundary condition,…
We derive and study a theoretical description for single file diffusion, i.e., diffusion in a one dimensional lattice of particles with hard core interaction. It is well known that for this system a tagged particle has anomalous diffusion…
It has been known since Lanford [19] that the dynamics of a hard sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to…
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…
In this paper we revisit the derivation of boundary conditions for the Boltzmann Equation. The interaction between the wall atoms and the gas molecules within a thin surface layer is described by a kinetic equation introduced in [9] and…
We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…
We consider the dynamic large deviation behaviour of Kac's collisional process for a range of initial conditions including equilibrium. We prove an upper bound with a rate function of the type which has previously been found for kinetic…
The problem of ballistic annihilation for a spatially homogeneous system is revisited within Boltzmann's kinetic theory in two and three dimensions. Exact analytical results are derived for the time evolution of the particle density for…
In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…
A simple kinematical argument suggests that the classical approximation may be inadequate to describe the evolution of a system with an anisotropic particle distribution. In order to verify this quantitatively, we study the Boltzmann…
A Boltzmann equation, used to describe the evolution of the density function of a gas of photons interacting by Compton scattering with electrons at low density and non relativistic equilibrium, is considered. A truncation of the very…
The diffraction-like process displayed by a spatially localized matter wave is here analyzed in a case where the free evolution is frustrated by the presence of hard-wall-type boundaries (beyond the initial localization region). The…
The purpose of this paper is to study the evolution of moving interacting particles on the mesoscopic scale. We will introduce an uncertainty principle and a new priori bound for the evolution of particles subject to a general mesoscopic…
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…
Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can…
In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in…