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Dichotomous Markov noise: Exact results for out-of-equilibrium systems

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Published in International Journal of Modern Physics. B. 2006, vol. 20, no. 20, p. 2825-2888
Abstract Nonequilibrium systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here some prototypical examples, with an emphasis on {em analytically-solvable} situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few relevant applications -- the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on a par with Gaussian white noise as far as obtaining analytical results is concerned. They convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to various practical applications.
Keywords Dichotomous Markov noiseStochastic processesFluctuationsNonequilibrium systemsColored noiseNoise-induced transitionsNoise-induced phase transitionsRatchetsNonlinear responseStokes' driftNoise-induced patternsMean-first passage timeStochastic resonance
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BENA COPPEX, Ioana Carla. Dichotomous Markov noise: Exact results for out-of-equilibrium systems. In: International Journal of Modern Physics. B, 2006, vol. 20, n° 20, p. 2825-2888. https://archive-ouverte.unige.ch/unige:86071

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Deposited on : 2016-08-16

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