A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field

2011/07/05 by Sébastien Breteaux, Breteaux, Sébastien
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Theoretical and Computational Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1107.0788

openalex publication_date 2011/07/05 · arxiv created 2012/06/25 · arxiv updated 2012/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 geometric and involves coherent states and semi-classical calculus.

Related

• Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrodinger Equation
• Beyond the Boltzmann equation for weakly coupled quantum fields
• On the derivation of the linear Boltzmann equation from the nonideal Rayleigh gas
• On the derivation of the Boltzmann equation in quantum field theory: Flat spacetime
• Boltzmann-Grad limit for the inelastic Lorentz gas: Part I. Existence, uniqueness, and rigorous derivation via weak convergence