Escape of Brownian particles and stochastic resonance with low-temperature quantum fluctuations

In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical compu...     

Current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation theory for the space-time fluctuations of the empirical current which include the previous results. We then estimate the probability of a fluctuation of the average current over a large time interval. It turns out that recent results by Bodineau and Derrida [Phys. Rev. Lett. 92, 180601 (2004)]] in certain cases underestimate this probability due to the occurrence of dynamical phase transitions.     

Overview: The constructive role of noise in fluctuation driven transport and stochastic resonance

Random noise is typically thought of as the enemy of order rather than as a constructive influence. Recent work has shown however that under certain circumstances, noise and Brownian motion can facilitate transmission of information via a mechanism know as stochastic resonance, and help systems use chemical energy and nonequilibrium fluctuations to drive directed motion via fluctuation driven transport. In this focus issue we have collected several articles that capture the flavor of these developing fields and point the way to new directions for research. (c) 1998 American Institute of Physics.     

The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

Coherence resonance and stochastic resonance in directionally coupled rings

In coupled systems, symmetry plays an important role for the collective dynamics. We investigate the dynamical response to noise with and without weak periodic modulation for two classes of ring systems. Each ring system consists of unidirectionally coupled bistable elements but in one class, the number of elements is even while in the other class the number is odd. Consequently, the rings without forcing show at a certain coupling strength, either ordering (similar to anti-ferromagnetic chains) or auto-oscillations. Analysing the bifurcations and fixed points of the two ring classes enables us to explain the dynamical response measured to noise and weak modulation. Moreover, by analysing a simplified model, we demonstrate that the response is universal for systems having a directional component in their stochastic dynamics in phase space around the origin.     

Nuclear stochastic resonance

Quantitative theory of the effect of nuclear ferromagnetism on the superconductivity of metals is proposed taking into account the electron-nuclear spin-spin interactions. At negative nuclear temperatures, when the nuclear magnetization is in opposition to an external magnetic field, nuclear ferromagnetism is favorable to superconductivity rather than suppressing it. The critical magnetic field in Be and TiH_2.07 hydrate metals may exceed the critical field of a nonmagnetic superconductor by an order of magnitude.     

Entropic stochastic resonance

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.     

Single-trigger stochastic resonance

Summary We discuss a recently discovered mechanism for stochastic resonance which involves only a single reference state with excitable dynamics and deterministic reinjection. While calculations based on an analogy with the shot effect capture the broadest features, detailed comparisons with specific dynamical systems suggest the need for certain refinements of the theory. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

Non-Markovian stochastic resonance

The phenomenological linear response theory of non-Markovian stochastic resonance (SR) is put forward for stationary two-state renewal processes. In terms of a derivation of a non-Markov regression theorem we evaluate the characteristic SR-quantifiers; i.e., the spectral power amplification (SPA) and the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian-SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive dependence of the SPA and SNR on small (adiabatic) driving frequencies; particularly, the adiabatic SNR becomes strongly suppressed over its Markovian counterpart. This non-Markovian SR-theory is elucidated for a fractal gating dynamics of a potassium ion channel possessing an infinite variance of closed sojourn times.     

Doubly stochastic resonance

We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.     

Nonlinear transport and dynamics of fluctuations

The time evolution of the macroscopic variables of a system initially in a state far from thermal equilibrium is studied from a statistical mechanical point of view. Exact nonlinear transport equations for the mean values and linear nonstationary Langevin equations for the fluctuations around the mean path are derived. Connections between the dynamics of fluctuations and the transport equations are discussed. The Langevin random forces depend on the macroscopic state and they are related to the transport kernels by a fluctuation-dissipation formula.     

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.     

Memory effects in stochastic transport

The memory effects in stochastic transport, namely, the dependence of the form of transport equations on the macroscopic time are considered. Equations explicitly taking into account the microscopic aspect of the problem, without which the transfer processes cannot be adequately described, are derived; the methods of their solution are suggested; and the asymptotic properties of the latter are analyzed.