We consider the motion of a Brownian particle in a tilted periodic potential with a fluctuating phase. The fluctuations are supposed to be either a nonstationary diffusion stochastic process or an Ornstein-Uhlenbeck process. In the latter case, the problem can be reduced to a system driven by additive "green" noise [Phys. Lett. A 240 (1998) 43]. The numerical results show that irreversible transitions from a locked (quasistationary) state to a running one (a fast drift) are very probable if the mass particle is large enough. For a given single realization of the external green noise a small change of system parameters may significantly alter the time at which the transition takes place. We call this phenomenon "a catastrophe". The numerical results are compared with those obtained by the Krylov-Bogoliubov averaging method. We found that the first approximation of the method is not sufficiently accurate if the irreversible transitions occur, and the coexistence between the locked and running states disappears. However, the averaged (effective) potential used in the averaging method remains an important tool to study the dynamics of systems driven by green noise. In particular, the switching between the states of the system occurs when the slow" rather than "fast" component of the particle motion reaches a local barrier of this potential. (C) 2003 Elsevier B.V. All rights reserved.
Catastrophes in brownian motion
MANNELLA, RICCARDO;
2003-01-01
Abstract
We consider the motion of a Brownian particle in a tilted periodic potential with a fluctuating phase. The fluctuations are supposed to be either a nonstationary diffusion stochastic process or an Ornstein-Uhlenbeck process. In the latter case, the problem can be reduced to a system driven by additive "green" noise [Phys. Lett. A 240 (1998) 43]. The numerical results show that irreversible transitions from a locked (quasistationary) state to a running one (a fast drift) are very probable if the mass particle is large enough. For a given single realization of the external green noise a small change of system parameters may significantly alter the time at which the transition takes place. We call this phenomenon "a catastrophe". The numerical results are compared with those obtained by the Krylov-Bogoliubov averaging method. We found that the first approximation of the method is not sufficiently accurate if the irreversible transitions occur, and the coexistence between the locked and running states disappears. However, the averaged (effective) potential used in the averaging method remains an important tool to study the dynamics of systems driven by green noise. In particular, the switching between the states of the system occurs when the slow" rather than "fast" component of the particle motion reaches a local barrier of this potential. (C) 2003 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
