  The purpose of this paper is to study the evolution of moving interacting
particles on the mesoscopic scale. We will introduce an uncertainty principle
and a new priori bound for the evolution of particles subject to a general
mesoscopic interaction and use this setting to demonstrate evidence for the
universal dispersion of particles in the absence of the conventional methods
like velocity averaging lemmas or Strichartz-type estimates. We will develop a
scattering theory in generality and use its frame work to show the existence
and uniqueness of a class scattering solutions to the Boltzmann equation with
asymptotic stability and completeness in the $L^{\infty}$ setting.
