A SEMICLASSICAL APPROACH TO THE KRAMERS--SMOLUCHOWSKI EQUATION.

We consider the Kramers--Smoluchowski equation at a low temperature regime and show how semiclassical techniques developed for the study of the Witten Laplacian and Fokker--Planck equation provide quantitative results. This equation comes from molecular dynamics and temperature plays the role of a semiclassical paramater. The presentation is self-contained in the one dimensional case, with pointers to the recent paper [L. Michel, About small eigenvalues of Witten Laplacian, preprint, https://arxiv.org/abs/1702.01837, 2018] for results needed in higher dimensions. One purpose of this note is to provide a simple introduction to semiclassical methods in this context. [ABSTRACT FROM AUTHOR]