Mathematical problems in the theory of Brownian motors

The Brownian (molecular) motors are the special systems driven by the external periodic or random fields. They can transform in the presence of the so-called ratchet mechanism the molecular chaos into the deterministic motion. This is one of the most popular subjects in the modern cell biology, chemical kinetics etc. The analysis of the corresponding mathematical problems includes the combination of the spectral theory, homogenization, complex analysis, large deviations technique etc.
The talk will contain the basic definitions, models and recent asymptotical results by me and Prof. B.Vainberg.