Noise induced patterning in reaction-diffusion systems with non-Fickian diffusion

We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. It is shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures. It was found that at small and large noise intensities the system is characterized by unstable homogeneous states. At intermediate values of the noise intensity three types of patterns are possible: nucleation, spinodal decomposition and stripes with liner defects (dislocations). Our analytical investigations are verified by computer simulations.     

Heat transfer between two nanoparticles through near field interaction

We introduce a thermal conductance by using the fluctuation-dissipation theorem to analyze the heat transfer between two nanoparticles separated by a submicron distance. Using either a molecular dynamics technique or a model based on the Coulomb interaction between fluctuating dipoles, we derive the thermal conductance. Both models agree for distances larger than a few diameters. For separation distances smaller than the particle diameter, we find a transition regime characterized by a thermal conductance larger than the contact conductance.     

Relaxation phenomena at criticality

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the thermodynamic control parameters. The non-equilibrium evolution following this change displays some of the features typically observed in glassy materials, such as ageing, and it can be monitored via dynamic susceptibilities and correlation functions of the order parameter, the scaling behaviour of which is characterized by universal exponents, scaling functions, and amplitude ratios. This universality allows one to calculate these quantities in suitable simplified models and field-theoretical methods are a natural and viable approach for this analysis. In addition, if a statistical system is spatially confined, universal Casimir-like forces acting on the confining surfaces emerge and they build up in time when the temperature of the system is tuned to its critical value. We review here some of the theoretical results that have been obtained in recent years for universal quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the Ising model with Glauber dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting in a film is discussed within the Gaussian model.     

Eulerian and Lagrangian Pictures of Non-equilibrium Diffusions

We show that a non-equilibrium diffusive dynamics in a finite-dimensional space takes in the Lagrangian frame of its mean local velocity an equilibrium form with the detailed balance property. This explains the equilibrium nature of the fluctuation-dissipation relations in that frame observed previously. The general considerations are illustrated on few examples of stochastic particle dynamics.     

Monte Carlo investigations of the influence of structural defects on aging effects and the violation of the fluctuation-dissipation theorem for a nonequilibrium critical behavior in the three-dimensional Ising model

The specific features of a nonequilibrium critical behavior in the three-dimensional structurally disordered Ising model have been studied numerically by the Monte Carlo method. An analysis of the two-time dependence of the autocorrelation function and the dynamic susceptibility for systems with spin concentrations p = 0.8 and 0.6 has revealed the aging effects, which are characterized by a slowing down of the relaxation of the system with an increase in the waiting time, and the violation of the fluctuation-dissipation theorem. The values of the universal limit of fluctuation-dissipation ratio for the considered systems have been obtained using the Monte Carlo method. It has been shown that the presence of structural defects in the system leads to an enhancement of the aging effects and to an increase of the values of the limit of fluctuation-dissipation ratio.     

Time reparametrization group and the long time behavior in quantum glassy systems

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( R(p)G) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.     

A general framework for non-equilibrium phenomena: the master equation and its formal consequences

We consider non-equilibrium systems defined by a state space, and by a stochastic dynamics and its stationary state. The dynamics need not satisfy detailed balance. In this abstract framework we do the following: (1) define and analyze “relative entropy”, (2) study dissipation in the relaxation to the stationary state, as well as the extra dissipation to maintain the system in its stationary state against some detailed balance dynamics, (3) extend the fluctuation-dissipation theorem and the Onsager relations, and (4) give a formula for the stationary state in terms of a summation over trees.     

Glassy properties of the Kawasaki dynamics of two-dimensional ferromagnets

We study numerically the Kawasaki dynamics of the 2D Ising model. At large time we recover the coarsening growth as l(c)(t) proportional t(1/3). At shorter time however, the system enters a metastable glassy regime that displays an extremely slow growth and nontrivial violations of the fluctuation-dissipation theorem similar to those observed in spin glasses: this is one of the simplest systems in which such violations occur. We also consider Potts models, where a similar behavior is observed, and the model of Shore and Sethna where the domain growth is also slow, but where violations of the fluctuation-dissipation theorem are trivial. We finally comment on these violations in the context of activated coarsening, and on similarities and differences with the glass transition phenomenology.     

Analysis of fusion-fission process with neutron evaporation in superheavy mass region

The fusion-fission process for the synthesis of superheavy elements is discussed on the basis of the fluctuation-dissipation dynamics. We analyze the experimental data using a three-dimensional Langevin calculation. We take the neutron emission into account in the Langevin calculation and compare the results with experimental data. Also we discuss the evaporation residue cross section for superheavy elements.     

Self-diffusion in sheared colloidal suspensions: violation of fluctuation-dissipation relation

Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e., Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature.     

Gravity fluctuations in studying the earth pole oscillation processes

Based on the dynamical Euler-Liouville equations, we consider a numerical-analytical model of the Earth pole oscillations in the first approximation under the gravitational tidal forces from the Sun and the Moon. The dynamics of the Earth pole motion is analyzed by taking into account the pole tide at the Chandler frequency. We note that allowance for the small fluctuation-dissipation perturbations due to the pole tide leads to variations in the Chandler component of the oscillations.     

Out-of-equilibrium microrheology inside living cells

Both forced and spontaneous motions of magnetic microbeads engulfed by Dictyostelium cells have served as experimental probes of intracellular dynamics. The complex shear modulus G*(omega), determined from active oscillatory measurements, has a power-law dynamics and increases with the probe size, reflecting intracellular structural complexity. The combined use of passive microrheology allows one to derive the power spectrum of active forces acting on intracellular phagosomes and to test the validity of the fluctuation-dissipation theorem inside living cells.     

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.     

Heterogeneous aging in spin glasses

We introduce a set of theoretical ideas that form the basis for an analytical framework capable of describing nonequilibrium dynamics in glassy systems. We test the resulting scenario by comparing its predictions with numerical simulations of short-range spin glasses. Local fluctuations and responses are shown to be connected by a generalized local out-of-equilibrium fluctuation-dissipation relation. Scaling relationships are uncovered for the slow evolution of heterogeneities at all time scales.     

Brownian Motion of a Charged Particle in Electromagnetic Fluctuations at Finite Temperature

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.     

Real-space application of the mean-field description of spin-glass dynamics

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard "mean-field theory" versus "droplet picture" debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.     

Calculation of the fluctuation-dissipation ratio for the nonequilibrium critical behavior of disordered systems

The values of a new universal parameter characterizing a nonequilibrium critical behavior, namely, the fluctuation-dissipation ratio specifying a fundamental relation between the dynamic response function and the correlation function, are calculated for the disordered three-dimensional Ising model. The analysis of the two-time dependence for autocorrelation functions and the ac susceptibility for the systems with spin densities p = 1.0, 0.8, and 0.6 shows the aging effects characterized by the anomalous slowing of relaxation in the system with the growth of the waiting time and the violation of the fluctuation-dissipation theorem. To improve the accuracy of the ac susceptibility calculations, the “thermal bath” technique has been used without introducing the applied magnetic field in the simulation. It has been shown that the structural defects lead to the pronounced enhancement of the aging effects.     

Fusion theory for synthesis of the superheavy elements

Recent developments on reaction mechanisms in fusion of massive systems are briefly reviewed, especially on a two-step model. The fusion hindrance observed experimentally is simply explained in connection with the fluctuation-dissipation dynamics of shape evolutions and of two-body collisions. Examples are given for fusion excitation functions and compared with the available data on ⁴⁸Ca+actinide target systems.