Effect of Initial Correlation on the Kinetic Equation

Abstract

In the bulk limit (particle number $N\ensuremath{\rightarrow}\ensuremath{\infty}$, volume $\ensuremath{\Omega}\ensuremath{\rightarrow}\ensuremath{\infty}$ with $\frac{N}{\ensuremath{\Omega}}\ensuremath{\mathrel{:=}}\mathrm{const}$), the one-body density operator $n(t)$ describing interacting distinguishable particles satisfied a closed evolution equation. This equation contains a set of terms which explicitly depend on the initial -correlation operators $\ensuremath{\chi}$, in contrast with a typical kinetic equation such as Boltzmann's equation. The nature of these terms is investigated. It is explicitly shown that the initial pair correlation ceases to influence the evolution of $n(t)$ after a time of the order of a collision duration for a weakly coupled low-density gas.