Geometric Analysis of the Linear Boltzmann Equation I. Trend to Equilibrium

On the Trend to Global Equilibrium for Spatially Inhomogeneous Kinetic Systems: the Boltzmann Equation

On the exponential decay to equilibrium of the degenerate linear Boltzmann equation

The dissipative linear Boltzmann equation

We introduce and discuss a linear Boltzmann equation describing dissipative interactions of a gas of test particles with a fixed background. For a pseudo-Maxwellian collision kernel, it is shown that, if the initial distribution has finite temperature, the solution converges exponentially for large–time to a Maxwellian profile drifting at the same velocity as field particles and with a universa...

Quantum linear Boltzmann equation

We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the cl...

On the Trend to Equilibrium for Solutions of the Boltzmann Equation : Quantitative Versions of Boltzmann’s H-theorem

The purpose of this article is to present some recent results on an old subject, namely the trend to thermodynamical equilibrium for solutions of the Boltzmann equation, with the help of the modern analytical tools coming from information theory and logarithmic Sobolev inequalities. Our main results were obtained in collaborations with L. Desvillettes and G. Toscani; they take their roots in pr...