The Evolution of a Tagged Particle in the Boltzmann--Grad Limit

Fraydoun Rezakhanlou
University of California, Berkeley (UC Berkeley)

Consider a system of hard spheres in thermal equilibrium. Using Lanford's method,

van Beijeren, Lanford, Lebowitz, and Spohn, showed that in the low-density (Boltzmann-Grad) limit, the total time correlation function is governed by the linearized Boltzmann equation provided that the time is sufficiently short. They also showed that the self time correlation function, equivalently the distribution of a tagged particle in an equilibrium fluid, is governed by the Rayleigh-Boltzmann equation. In this talk, I give a new proof of the latter result which uses velocity averaging techniques and does not rely on BBGKY hierarchy equations. The hope is that the method may apply to the total time correlation function without any short time restriction.

This would resolve a long-standing open problem in this context.

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