Mathematical Physics and Harmonic Analysis Seminar

Date: March 19, 2025

Time: 2:00PM - 2:50PM

Location: BLOC 302

Speaker: Matt Powell, Georgia Institute of Technology

Title: A coupled 3d Kac evolution and its approach to equilibrium

Abstract: In 1956 Mark Kac introduced a simple model for the evolution of a gas of hard spheres undergoing elastic collisions. The Kac master equation, due to its simplicity, occupies a special place among the models describing a gas of interacting particles. Its many uses includes providing a reasonably satisfactory derivation of the spatially homogeneous Boltzmann equation and giving a mathematical framework for investigating the approach to equilibrium. These issues were, in fact, the motivation for Kac’s original work. The classical Kac master equation is a 1D model based on simple probabilistic principles and yields a linear evolution equation for the velocity distribution for N 1-dimensional particles undergoing collisions. In this talk, we will discuss new and ongoing work studying properties of a 3-dimensional Kac evolution, the analysis of which differs from that of the original 1-dimensional model due to additional conservation laws. These results are all joint with F. Bonetto and M. Loss.