Brownian motors: How noise is transfered into transport
R. Bartussek, P. Reimann, and P. Hänggi
University of Augsburg, Department of Physics,
Memminger Str. 6, D-86135 Augsburg, Germany
The fact that random noise can be useful rather than a nuisance has been demonstrated by the effect of Stochastic Resonance (SR). A further example for this are the so called `Brownian Motors' which are extensively studied now since several years [e.g.,1-5]. The idea behind it is to obtain a mean drift in a periodic potential by applying only forces of zero temporal mean. Thermal noise can then enhance the deterministic drift speed of a particle or can even be a necessary ingredient to obtain a mean drift at all. However, thermal noise by itself can not be enough to obtain a mean velocity (the second law of thermodynamics forbids it!): A possibility to achieve this is to use a potential without spatial symmetry (`Ratchet' potential) and to bring correlations into the system (e.g., through a periodic driving force[1], or by varying the height of the potential in a correlated manner[2]). A different mechanism based on asymmetric noise of zero average applies to potentials that obey reflection symmetry, see [3].
In our model we describe the overdamped motion of a particle along a Ratchet potential. The particle feels additive white, Gaussian noise, and also additive colored noise - in our model Ornstein-Uhlenbeck noise. Numerical results for the mean velocity of the particle are compared with several analytical approximations, namely the Unified Colored Noise approximation and different path integral approximations.
Our main findings are, that for a properly chosen ratchet potential
the direction of the current can change its sign when
the correlation time of the colored noise is varied.
Hence for this current reversal it is not necessary to change general properties
of the colored noise as it was in previous publications:
Here it is not necessary to change the distribution of the noise [4],
or to change the sign of a derivative of the colored noise spectrum [5].
We further find parameter regions where with increasing white noise intensity
( 
temperature) the mean velocity increases -
noise is helpful as it is in SR.
We also investigate the dependence of the mean velocity against an applied constant force (equivalent to tilting the potential). These results can be compared with measurements in biological systems, such as the motion of kinesin along a Microtubulus.
uczka, R. Bartussek, and P. Hänggi, Europhys. Lett. 31
(1995) 431.