Kramers Equation and Supersymmetry

Hamilton’s equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories in an elementary way. From a more practical point of view, the formalism provides new tools to study the reaction paths in systems with separated time scales. A ‘reduced current’ which contains the relevant part of the phase space probability current is introduced, together with strategies for its computation.