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.     

Two time scales and violation of the fluctuation-dissipation theorem in a finite dimensional model for structural glasses

We study the breakdown of fluctuation-dissipation relations between time-dependent density-density correlations and associated responses following a quench in the chemical potential in the frustrated Ising lattice gas. The corresponding slow dynamics is characterized by two well-separated time scales characterized by a constant value of the fluctuation-dissipation ratio. This result is particularly relevant since activated processes dominate the long-time dynamics of the system.     

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.     

Fluctuation-dissipation theorem in an aging colloidal glass

We provide a direct experimental test of the fluctuation-dissipation theorem (FDT) in an aging colloidal glass. The use of combined active and passive microrheology allows us to independently measure both the correlation and response functions in this nonequilibrium situation. Contrary to previous reports, we find no deviations from the FDT over several decades in frequency (1 Hz-10 kHz) and for all aging times. In addition, we find two distinct viscoelastic contributions in the aging glass, including a nearly elastic response at low frequencies that grows during aging.     

Efficient measurement of linear susceptibilities in molecular simulations: application to aging supercooled liquids

We propose a novel method to measure time-dependent linear susceptibilities in molecular simulations, which does not require the use of nonequilibrium simulations, subtraction techniques, or fluctuation-dissipation theorems. The main idea is an exact reformulation of linearly perturbed quantities in terms of observables accessible in a single unperturbed trajectory. We apply these ideas to supercooled liquids in a nonequilibrium aging regime. We show that previous work had underestimated deviations from fluctuation-dissipation relations in the case of a Lennard-Jones system, while our results for silica are in qualitative disagreement with earlier results.     

Generalized Einstein Relation in an aging colloidal glass

We present an experimental investigation of the Generalized Einstein Relation (GER), a particular form of a fluctuation-dissipation relation, in an out-of-equilibrium visco-elastic fluid. Micrometer beads, used as thermometers, are immersed in an aging colloidal glass to provide both fluctuation and dissipation measurements. The deviations from the Generalized Einstein Relation are derived as a function of frequency and aging time. The observed deviations are interpreted as directly related to the change in the glass relaxation times with aging time. In our scenario, deviations are observed in the regime where the observation timescale is of the order of a characteristic relaxation time of the glass.     

Fluctuation-dissipation ratio in three-dimensional spin glasses

We present an analysis of the data on aging in the three-dimensional Edwards-Anderson spin-glass model with nearest-neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean-field theory. We measure the parameterx(q) describing the violation of the relation among correlation and response functions implied by the fluctuation-dissipation theorem.     

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.     

Fluctuation-dissipation theorem in liquid and glassy glycerol: frequency-dependent dielectric permittivity and dielectric polarization fluctuation measurements

We show frequency-dependent dielectric permittivity and dielectric polarization fluctuation measurements of liquid and glassy glycerol. This allows a direct comparison of both quantities determined independently. After cooling the glycerol sample to 179 K with a cooling rate of 0.85 K/min we studied the aging time dependence of the dielectric permittivity and the polarization fluctuations using the identical glycerol sample. A cross-correlation technique allows measurements of noise levels below the amplifier noise. In the frequency range between 0.3 and 300 Hz we find the measured data to be in agreement with the fluctuation-dissipation theorem for the liquid and glassy state not depending on the aging time.     

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.     

Fluctuation-dissipation theorems for systems in non-thermal equilibrium and applications

The linear response theory of systems obeying Fokker-Planck equations is discussed under the assumption that the principle of detailed balance is satisfied. This theory is used to obtain fluctuation-dissipation theorems for systems in a non-thermal equilibrium state corresponding to the steady state solution of the Fokker-Planck equation. Some of the aspects of the threshold region of a single mode laser (without detuning) are discussed. In particular it is shown that, contrary to the results established recently by others, the “linear susceptibility” χ(Ω) is acontinuous function of the pump parameterp. The results are then specialized to Gaussian Markov process in which case an alternate form of the fluctuation-dissipation theorems is also given. Finally few other generalizations of the fluctuation-dissipation theorems are also briefly discussed.     

Experimental evidence for violation of the fluctuation-dissipation theorem in a superspin glass

We present the experimental observation of the fluctuation-dissipation theorem violation in an assembly of interacting magnetic nanoparticles in the low temperature superspin-glass phase. The magnetic noise is measured with a two-dimension electron gas Hall probe and compared to the out of phase ac susceptibility of the same ferrofluid. For "intermediate" aging times of the order of 1 h, the ratio of the effective temperature T(eff) to the bath temperature T grows from 1 to 6.5 when T is lowered from T(g) to 0.3 T(g), regardless of the noise frequency. These values are comparable to those measured in an atomic spin glass as well as those calculated for a Heisenberg spin glass.     

闭路格林函数和非线性响应理论(Ⅱ)

本文是关于非线性响应理论的文章的后半部分。我们利用文献[1]的结果将线性情形的涨落耗散定理形式地推广到含有n点关联和响应函数的非线性情形。 关键词：     

Asymmetric response of a jammed plastic bead raft

The successful development of an effective temperature would be an important step in the application of statistical mechanics principles to systems driven far from equilibrium. One direction that has shown promise is the use of fluctuation-dissipation relations. However, driven systems break time-reversal symmetry, and understanding the implications of this for fluctuation-dissipation relations is a critical step in developing effective temperatures. Here we study the response function in a driven system of plastic beads as a function of the density in order to elucidate the generality of the use of fluctuation-dissipation relations. We find that even when a linear response is observed, the time scale of the response is dependent on the direction of the applied stress.     

Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales. A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.     

On Viscosity and Fluctuation-Dissipation in Exclusion Processes

We consider the asymmetric simple exclusion process. We review some results in dimension d≥3 concerning the fluctuation-dissipation theorem and we prove regularity of viscosity coefficients.     

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the ‘fluctuation-dissipation theorem’, the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the ‘fluctuation-dissipation theorem’ is satisfied, and this verifies that satisfying ‘fluctuation-dissipation theorem’ indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.     

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.     

Effective temperature and fluctuation-dissipation theorem in athermal granular systems:A review

The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.