Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise

In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise.     

Noise-induced collective regimes of complex system in contact with a random reservoir

Based on a system-reservoir model, where the reservoir is driven by an external white Gaussian noise, we study the behavior of system components in Weiss mean-field approach and Gaussian approximation for moments. Crossover from individual to cooperative dynamics of the system components is due to noise. The system displays a transition similar to diversity-induced phase transition. The analytical results are compared with the numerical simulations.     

Noise-induced coupling and phase transition in initially homogeneous bistable system

We show that a colored spatial noise induces a heterogeneous behavior and coupling of initially uncoupled single bistable units. A formal approximation reduces a non-Markovian stochastic process described by the initial set of equations into Markovian process in terms of Langevin equation, for which a simple piecewise linear emulation was used to represent the nonlinear deterministic force. It turned out that the coupling leads to a phase transition due to the noise-induced diffusive term. As an example, a typical bistable noisy system with symmetric double-well potential was studied.     

Escape for System with Non-Fluctuating Potential Barrier Only Driven by Three-State Noise

We study the escape for the mean first passage time （MFPT） over a potential barrier for a system with non- fluctuating potential barrier and only driven by a three-state noise. It is shown that in some circumstances, the three-state noise can induce the resonant activation for the MFPT over the potential barrier; but in other circumstances, it can not. There are three resonant activations for the MFPT over the potential barrier, which are respectively as the functions of the transition rates of the three-state noise.     

Transverse diffusion induced phase transition in asymmetric exclusion process on a surface

We extend one-dimensional asymmetric simple exclusion process (ASEP) to a surface and show that the effect of transverse diffusion is to induce a continuous phase transition from a constant density phase to a maximal current phase as the forward transition probability p is tuned. The signature of the non-equilibrium transition is evident in the finite size effects near the transition. The results are compared with similar couplings operative only at the boundary. It is argued that the nature of the phases can be interpreted in terms of the modifications of boundary layers.     

Deterministic escape of a dimer over an anharmonic potential barrier

In the present paper we consider the deterministic escape dynamics of a dimer from a metastable state over an anharmonic potential barrier. The underlying dynamics is conservative and noiseless and thus, the allocated energy has to suffice for barrier crossing. The two particles comprising the dimer are coupled through a spring. Their motion takes place in a two-dimensional plane. Each of the two constituents for itself is unable to escape, but as the outcome of strongly chaotic coupled dynamics the two particles exchange energy in such a way that eventually exit from the domain of attraction may be promoted. We calculate the corresponding critical dimer configuration as the transition state and its associated activation energy vital for barrier crossing. It is found that there exists a bounded region in the parameter space where a fast escape entailed by chaotic dynamics is observed. Interestingly, outside this region the system can show Fermi resonance which, however turns out to impede fast escape.     

Fluctuation-driven directed transport in the presence of Lévy flights

The role of Lévy flights on fluctuation-driven transport in time independent periodic potentials with broken spatial symmetry is studied. Two complementary approaches are followed. The first one is based on a generalized Langevin model describing overdamped dynamics in a ratchet type external potential driven by Lévy white noise with stability index α in the range 1<α<2. The second approach is based on the space fractional Fokker-Planck equation describing the corresponding probability density function (PDF) of particle displacements. It is observed that, even in the absence of an external tilting force or a bias in the noise, the Lévy flights drive the system out of the thermodynamic equilibrium and generate an up-hill current (i.e., a current in the direction of the steeper side of the asymmetric potential). For small values of the noise intensity there is an optimal value of α yielding the maximum current. The direction and magnitude of the current can be manipulated by changing the Lévy noise asymmetry and the potential asymmetry. For a sharply localized initial condition, the PDF of staying at the minimum of the potential exhibits scaling behavior in time with an exponent bigger than the −1/α exponent corresponding to the force free case.     

Transport and dynamical properties of inertial ratchets

In this paper we discuss the dynamics and transport properties of a massive particle in a ratchet type potential immersed in a dissipative environment. The directional currents and characteristics of the motion are studied as the specific frictional coefficient varies, finding that the stationary regime is strongly dependent on this parameter. The maximal Lyapunov exponent and the current show large fluctuations and inversions, therefore for some range of the control parameter, this inertial ratchet could originate a mass separation device. Also an exploration of the effect of a random force on the system is performed.     

Stochastic resonance and heat fluctuations in a driven double-well system

We study a periodically driven (symmetric as well as asymmetric) double-well potential system at finite temperature. We show that mean heat loss by the system to the environment (bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat loss over a large number of periods satisfies the conventional steady-state fluctuation theorem.     

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.     

Energy dissipation and violation of the fluctuation-response relation for harmonic oscillators described by the generalized Langevin equation

The generalized Langevin equation (GLE) satisfied by harmonic oscillators coupled to a heat bath is transformed into an equality between the rate of energy dissipation and an extent of violation of the fluctuation-response relation. Its significance is discussed. When the system reaches a stationary state and a single harmonic oscillator’s frequency is set to zero, the equality reduces to a fluctuation-dissipation relation, which is slightly different from the usual Kubo’s formalism.     

Correlated noises in an absorptive optical bistable model

We study the steady state properties of an absorptive optical bistable model in the presence of correlated noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution and the average value of the transmitted light have been investigated. We have found that fluctuations of the input light amplitude improve the transmitted light and an optimized value exists for the fluctuations of the population difference at which the transmitted light takes its maximum value. The correlation between the two noises reduce the transmitted light and the noises in the model can induce a phase transition.     

Resonant regions of Josephson junction equation in case of large damping

The dynamics of Josephson junction equation in case of damping α>2 is investigated numerically. In this case the second-order system can be asymptotically reduced in the large to a one-dimensional circle map. We study the parametric dependence of the resonances of this system and plot the resonant regions in two-dimensional parameter space. The periodic variation of the widths of harmonic regions with increase of the periodic driving force is observed. In the limit of infinite damping, we study a first order system through suitable re-scaling and the same property is observed. We conjecture this may caused by the competition between the periodic potential and the periodic external driving in these systems.     

Transport reversal in a delayed feedback ratchet

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here the dynamics of a feedback flashing ratchet when the asymmetry of the ratchet potential and of the feedback protocol favor transport in opposite directions. The introduction of a time delay in the control strategy allows one to nontrivially tune the relative relevance of the competing asymmetries leading to an interesting dynamics. We show that the competition between the asymmetries leads to a current reversal for large delays. For small ensembles of particles current reversal appears as the consequence of the emergence of an open-loop like dynamical regime, while for large ensembles of particles it can be understood as a consequence of the stabilization of quasiperiodic solutions. We also comment on the experimental feasibility of these feedback ratchets and their potential applications.     

Phase diagram and scattering intensity of binary amphiphilic systems

A Ginzburg-Landau model with a scalar and a vector order parameter, which describe the concentration and orientation of the amphiphile, respectively, is used to study the phase diagram and the scattering intensity of binary amphiphilic systems. With increasing amphiphile concentration, the calculated phase diagram shows the typical sequence of ordered phases observed experimentally, that is micellar liquid cubic micellar hexagonal lamellar cubic bicontinuous invers hexagonal. The scattering intensity in the homogeneous phase is calculated in the oneloop approximation. In the vicinity of a phase transition to an ordered phase, the intensity is found to show a 1/q behavior for not too small wave vectorsq, followed by a small peak, and a 1/q ² decay for large wave vectors, in agreement with experimental observations in theL ₃-(or sponge-)phase.Dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.     

On a super-diffusive, nonlinear birth and death process

The explicit and fully analytic transient solution for the transition probability density associated with a nonlinear birth and death process on Z is constructed. The time-dependent variance is proportional to t+Bt² (with B being a constant), thus exhibiting a super-diffusive behavior. The space continuous limit of this process is a well-known diffusion process with nonlinear drift for which the transition probability density is also known explicitly in a very simple way.     

Phase transition in annihilation-limited processes

A system of particles is studied in which the stochastic processes are one-particle type-change (or one-particle diffusion) and multi-particle annihilation. It is shown that, if the annihilation rate tends to zero but the initial values of the average number of the particles tend to infinity, so that the annihilation rate times a certain power of the initial values of the average number of the particles remain constant (the double scaling) then if the initial state of the system is a multi-Poisson distribution, the system always remains in a state of multi-Poisson distribution, but with evolving parameters. The large time behavior of the system is also investigated. The system exhibits a dynamical phase transition. It is seen that for a k-particle annihilation, if k is larger than a critical value k_c, which is determined by the type-change rates, then annihilation does not enter the relaxation exponent of the system; while for k < k_c, it is the annihilation (in fact k itself) which determines the relaxation exponent.