Small Mass Asymptotics for a Charged Particle in a Magnetic Field and Long-Time Influence of Small Perturbations

We consider small mass asymptotics of the motion of a charged particle in a potential combined with a magnetic field. After an appropriate regularization, a Smoluchowski-Kramers type approximation is established. This approximation allows to study long-time influence on the motion of various perturbations, deterministic and stochastic. In particular, even in the case of pure deterministic perturbations, the long-time evolution of the perturbed system can be stochastic.