Motion reversal of molecular motor assemblies due to weak noise

Bidirectional motion is an example of collective behavior of molecular motors. It occurs at finite noise level in a nonequilibrium system. We consider this problem as a first exit problem. We identify the noise strength by doing an expansion of a master equation and apply the Wentzell-Freidlin theory to define an effective nonequilibrium potential and provide analytical estimates of the reversal time. Our results match very well with the results of stochastic simulations.     

Non-Markovian stochastic processes: colored noise

We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.     

Response of spin-accumulated ferromagnet/superconductor/ferromagnet double tunnel junction to applied magnetic field

Tunneling current in a ferromagnet/superconductor/ferromagnet double tunnel junction induces a nonequilibrium spin accumulation in the superconductor. We study theoretically the response of such a system to applied magnetic field. We show that the interplay between the magnetic field and the spin accumulation could lead to novel bias voltage dependence and magnetic field dependence of the superconducting gap function, and bring in anomalous asymmetry in the spin-dependent transport. Our study also indicates a possible application of the spin injection.     

Hydrodynamic Fluctuations in Laminar Fluid Flow. I. Fluctuating Orr-Sommerfeld Equation

In recent years it has become evident that fluctuating hydrodynamics predicts that fluctuations in nonequilibrium states are always spatially long ranged. In this paper we consider the application of fluctuating hydrodynamics to laminar fluid flow, using plane Couette flow as a representative example. Specifically, fluctuating hydrodynamics yields a stochastic Orr-Sommerfeld equation for the wall-normal velocity fluctuations, where spontaneous thermal noise acts as a random source.This stochastic equation needs to be solved subject to appropriate boundary conditions. We show how an exact solution can be obtained from an expansion in terms of the eigenfunctions of the Orr-Sommerfeld hydrodynamic operator. We demonstrate the presence of a flow-induced enhancement of the wall-normal velocity fluctuations and a resulting flow-induced energy amplification and provide a quantitative analysis how these quantities depend on wave number and Reynolds number.     

A non-linear stochastic differential equation: Exact critical statics and dynamics

The nonlinear stochastic differential equation we present is a generalization of a class of equations describing various physical and chemical systems coupled to external sources of noise.The static behaviour of this system exhibits first and second order nonequilibrium transitions which are purely induced by the external noise. Exact analytical expressions for the time dependent solutions are found.     

Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic part, the latter being performed by sampling exactly the solution of the associated Fokker-Planck equation. We demonstrate the computational power of this method by applying it to the most absorbing phase transitions for which Langevin equations have been proposed. This provides precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.     

Flicker Noise in a Locally Nonequilibrium Medium

A model implying that particles of a medium are subjected to external forces with a flicker noise spectrum has been proposed to describe fluctuations in locally nonequilibrium physical media. The Langevin equation with additional integral terms describing the action of the locally nonequilibrium medium has been derived. The spectral density of fluctuations of an electric current flowing in the locally nonequilibrium medium has been calculated. It has been found that this density in the low-frequency spectral range is flicker noise.     

Nonequilibrium Shot Noise Spectrum Through a Quantum Dot in the Kondo Regime:A Master Equation Approach under Self-Consistent Born Approximation

We construct a number(n)-resolved master equation(ME)approach under self-consistent Born approximation(SCBA)for noise spectrum calculation.The formulation is essentially non-Markovian and incorporates properly the interlay of the multi-tunneling processes and many-body correlations.We apply this approach to the challenging nonequilibrium Kondo system and predict a profound nonequilibrium Kondo signature in the shot noise spectrum.The proposed n-SCBA-ME scheme goes completely beyond the scope of the Born-Markovian master equation approach,in the sense of being applicable to the shot noise of transport under small bias voltage,in non-Markovian regime,and with strong Coulomb correlations as favorably demonstrated in the nonequilibrium Kondo system.     

Pumped biochemical reactions, nonequilibrium circulation, and stochastic resonance

Based on a master equation formalism for mesoscopic, unimolecular biochemical reactions, we show the periodic oscillation arising from severe nonequilibrium pumping is intimately related to the periodic motion in recently studied stochastic resonance (SR). The white noise in SR is naturally identified with the temperature in the biochemical reactions; the drift in the SR is associated with the circular flux in nonequilibrium steady state (NESS). As in SR, an optimal temperature for biochemical oscillation is shown to exist. A unifying framework for Hill's theory of NESS and the SR without periodic forcing is presented. The new formalism provides an analytically solvable model for SR.     

Long-range triplet Josephson current driven by the bias voltage

We study the long-range triplet Josephson current in a clean junction composed of two s-wave superconductors and a normal-metal/ferromagnet/normal-metal trilayer. Through applying the bias voltages on the metal regions by two antiparallel half-metal electrodes, we show that the amplitude and direction of this long-range current can be controlled flexibly. Such current arises from the fact that the applied voltage can produce a nonequilibrium spin-dependent quasiparticle distribution in the metal regions so that the Cooper pairs entering these regions acquire extra momenta, which will lead to a spin-transition process in the metal regions. This process can produce the parallel spin-triplet pairs in the central ferromagnet layer. In particular, if the voltage is applied only to one metal region, we further find that the recently discovered long-range superharmonic Josephson current will appear because of the transport of an even number of parallel spin-triplet pairs.     

Perturbation Theory for Continuous Stochastic Equations

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probaibility distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes. stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion - controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and nonequilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered.     

Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.     

Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.     

Spin polarized current in the ground state of superconductor-ferromagnet-insulator trilayers

We study the ground state properties of a superconductor-ferromagnet-insulator trilayer on the basis of a Hubbard Model featuring exchange splitting in the ferromagnet and electron-electron attraction in the superconductor. We solve the spin-polarized Hartree-Fock-Gorkov equations together with the Maxwell's equation (Ampere's law) fully self-consistently with respect to the order parameter and the current. For certain values of the exchange splitting we find that a spontaneous spin polarized current is generated in the ground state and is intimately related to Andreev bound states at the Fermi level. Moreover, the polarization of the current strongly depends on the band filling. Received 23 September 2002 / Received in final form 13 December 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: m.a.krawiec@bristol.ac.uk     

Stable nonequilibrium probability densities and phase transitions for meanfield models in the thermodynamic limit

A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered.     

Relationship between a non-Markovian process and Fokker–Planck equation

We demonstrate the equivalence of a non-Markovian evolution equation with a linear memory-coupling and a Fokker–Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different, but representative initial distributions. The analytical calculations are supported by numerical results.     

铁磁-绝缘层-铁磁-d波超导结中的量子干涉效应对微分电导与散粒噪声的影响

通过求解BogoliubovedeGennes(BdG)方程,利用推广的BlonderTinkhamKlapwijk(BTK)理论,计算铁磁绝缘层铁磁d波超导结中的微分电导、平均电流和散粒噪声功率.研究表明,系统的微分电导和散粒噪声与平均电流的比值都随中间铁磁层厚度作周期性振荡,振荡的幅度随绝缘层势垒增高而变大,随铁磁层中磁交换劈裂的增强而变小. 关键词： 微分电导 散粒噪声 磁交换劈裂