Smoluchowski–Kramers approximation with state dependent damping and highly random oscillation

Abstract

<p style='text-indent:20px;'>The small mass limit (Smoluchowski–Kramers approximation) of class systems of ordinary differential equations describing motions of small mass particle with state dependent friction and high oscillation is derived by a diffusion approximation approach. In the small mass limit, due to the state dependent damping, one additional term appears in the limit equation, which leads to a stochastic differential equation (SDE) as the highly random oscillation appears as a multiplicative white noise.</p>