Rate description of Fokker-Planck processes with time-periodic parameters

The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific probability densities and localizing functions can be associated to each metastable state. Together, these three sets of functions uniquely characterize the large time dynamics of the conditional probability density of the original process. Exact equations of motion are formulated for these three sets of functions and strategies are discussed how to solve them. These methods are illustrated and their usefulness is demonstrated by means of the example of a bistable Brownian oscillator within a large range of driving frequencies from the slow semiadiabatic to the fast driving regime

Langevin dynamics with dichotomous noise; direct simulation and applications

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen

An Investigation of Stochastic Cooling in the Framework of Control Theory

This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling system must be considered as a closed-loop, similar to the feedback systems used to damp collective instabilities. These systems, which are able to act upon themselves, are potentially unstable. The self-consistent solution for the beam motion is derived by means of a mode analysis of the collective beam motion. This solution yields a criterion for the stability of each collective mode. The expressions also allow for overlapping frequency bands in the beam spectrum and thus are valid over the entire frequency range. Having established the boundaries of stability in this way, the Fokker-Planck equation is used to describe the cooling process. This description does not include collective effects and thus a stable beam must be assumed. Hence the predictions about the cooling process following from the Fokker-Planck equation only make physical sense within the boundaries of beam stability. Finally it is verified that the parameters of the cooling system which give the best cooling results are compatible with the stability of the beam.Comment: 64 pages, latex, 11 eps-figures appended as uuencoded file, german hyphenation corrected I

Voltage noise, switching rates, and multiple phase-slips in moderately damped Josephson junctions

We study the voltage noise properties including the switching rates and statistics of phase-slips in moderately damped Josephson junctions using a novel efficient numerical approach combining the matrix continued-fraction method with the full counting statistics. By analyzing the noise results obtained for the RCSJ model we identify different dominating components, namely the thermal noise close to equilibrium (small current-bias regime), the shot noise of (multiple) phase-slips in the intermediate range of biases and the switching noise for yet higher bias currents. We extract thus far inaccessible characteristic rates of phase-slips in the shot noise regime as well as the escape and retrapping rates in the switching regime as functions of various junction's parameters. The method can be extended and applied to other experimentally relevant Josephson junction circuits.Comment: 5 pages, 4 figures of the main text + 7 pages of supplemen

Levy ratchets with dichotomic random flashing

Additive symmetric L\'evy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such L\'evy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the L\'evy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static L\'evy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive L\'evy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.Comment: 15 pages, 6 figure

Transport and bistable kinetics of a Brownian particle in a nonequilibrium environment

A system reservoir model, where the associated reservoir is modulated by an external colored random force, is proposed to study the transport of an overdamped Brownian particle in a periodic potential. We then derive the analytical expression for the average velocity, mobility, and diffusion rate. The bistable kinetics and escape rate from a metastable state in the overdamped region are studied consequently. By numerical simulation we then demonstrate that our analytical escape rate is in good agreement with that of numerical result.Comment: 10 pages, 2 figures, RevTex4, minor correction