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Register a new userCurrent fluctuations in stochastic systems with long-range memory
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We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation function in analogy with long-range spatial correlations in equilibrium systems. We give some illuminating examples and discuss the applicability of the Gallavotti-Cohen fluctuation theorem.
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We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large deviation principle describing the probability of rare currents and show how superdiffusive behaviour can emerge. We illustrate the general framework with detailed calculations for a memory-dependent version of the totally asymmetric simple exclusion process as well as indicating connections to other recent work.
In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay <y(t) y(t+T)>=1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) the process y(t), although Markovian, is long-range correlated. Our results help in clarifying that even in the context of Markovian processes long-range dependencies are not necessarily associated to the occurrence of extreme events. Moreover, our results can be relevant in the modeling of complex systems with long memory. In fact, we provide simple processes associated to Langevin equations thus showing that long-memory effects can be modeled in the context of continuous time stationary Markovian processes.
We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-alpha}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $alpha$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $alpha <2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $alpha geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($alpha=1$) and dipolar magnetic films ($alpha=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.
Temperature
We investigate a particular phase transition between two different tunneling regimes, direct and injection (Fowler-Nordheim), experimentally observed in the current-voltage characteristics of the light receptor bacteriorhodopsin (bR). Here, the sharp increase of the current above about 3 V is theoretically interpreted as the cross-over between the direct and injection sequential-tunneling regimes. Theory also predicts a very special behaviour for the associated current fluctuations around steady state. We find the remarkable result that in a large range of bias around the transition between the two tunneling regimes, the probability density functions can be traced back to the generalization of the Gumbel distribution. This non-Gaussian distribution is the universal standard to describe fluctuations under extreme conditions.
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