Weak coupling limit for a tracer particle with rapid scatterings by light particles with point interactions

The primary result of this dissertation is a rigorous analysis of a scattering process for a test particle in the weak coupling limit. The reduced dynamics of the scattering process describes the free dynamics of a particle in 1 or 3 dimensions interlaced with scatterings with particles whose interaction is given by a point potential; the limiting dynamics describes a particle in an electro-magnetic field with an idealized non-classical noise. The weak coupling limit arises by taking the mass ratio lambda = mM of a single scattering particle to the test particle to be near zero while the frequency of collisions increases proportionally to 1l . The limiting dynamics is accurate up to second order in lambda and the strength of both the vector potential of the induced electromagnetic field and the white noise is proportional to lambda. We conjecture that after a second limit corresponding to a gas reservoir in an equilibrium state, the dynamics converge to a form studied for decoherence by Gallis and Fleming in 1990. We conclude by discussing decoherence related quantities of these limiting equilibrium dynamics.