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Proceedings Paper

Brownian motion in tilted periodic potential driven by green impulse noise
Author(s): Sergey A. Guz; Michael G. Nikulin; Michael V. Sviridov
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Paper Abstract

We study a Brownian overdamped motion driven by the sequence of non-Gaussian correlated random impulses. A main characteristic of this external noise is that a following impulse has strictly opposed sign relative to the previous one. It is generated by a time derivative of stationary random jump function that may be equal or similar to a random telegraphic signal. Therefore, the noise is "green" by definition [Phys. Lett. A240 (1998) 43]. In order to find the mean drift velocity of a Brownian particle we employ two approaches: a Krylov-Bogolubov averaging method and a numerical simulation. The first method is used for the case of the jump function to be the random telegraphic signal. Then the probability dis-tribution density that describes statistics of time interval between the delta-function impulses of external noise is an ex-ponential function. The numerical calculation is performed by means of using the narrow rectangular impulse instead of the delta-function. We consider two models of such noise. In the first case the distribution density of time interval be-tween the rectangular impulses is again described by the exponential function. In other case the interval is uniformly distributed. We show that a locking effect (or a synchronization) exists even if a mean frequency of impulses is small. This effect exists with a high accuracy even if noise is strong. According to the theory an effective locking band is equal to the cosine of the amplitude of the original jump function. In particular, if the amplitude is π, the band is zero, how-ever, if it is equal to π, the band is unity as well as in the ideal case of zero noise. It is interesting that this property holds true even if the averaging method becomes inapplicable. We show also that the theory good coincide with the numerical simulation.

Paper Details

Date Published: 3 January 2007
PDF: 8 pages
Proc. SPIE 6417, Complexity and Nonlinear Dynamics, 641708 (3 January 2007); doi: 10.1117/12.693215
Show Author Affiliations
Sergey A. Guz, Moscow Institute of Physics and Technology (Russia)
Michael G. Nikulin, Moscow Institute of Physics and Technology (Russia)
Michael V. Sviridov, Moscow Institute of Physics and Technology (Russia)

Published in SPIE Proceedings Vol. 6417:
Complexity and Nonlinear Dynamics
Axel Bender, Editor(s)

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