Symmetry properties of brownian motors with fluctuating periodic potential energy
Abstract
We consider the inertialess motion of a Brownian particle in a potential field described by an arbitrary periodic function of coordinate and time. The first terms of an expansion of the average particle velocity over the small parameter, which is the ratio of changes of the potential energy amplitude to the thermal energy, have been represented, that is, the expression for the high-temperature Brownian motor average velocity. The analysis of those expressions revealed the vector and shift symmetry as well as the hidden space-time symmetry of Cubero- Renzoni (D.Cubero, F.Renzoni). These symmetry types have been used to analyze space-time dependences of potential energy which prevent appearance of ratchet effect. We also study the additional types of symmetry, which are inherent in adiabatically slow and fast Brownian motors, as well as the conditions for the potential energy at which the average motor velocity becomes zero.
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