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.     

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.     

Extension of the fluctuation-dissipation theorem to non-equilibrium systems

The fluctuation-dissipation theorem is generalized to the case of nonequilibrium (albeit in a stable steady state) systems. The relationship between the correlation function of the current fluctuations and the average energy absorbed by the system as a consequence of dissipation is used. For a nonequilibrium classical system, the responce function is connected with the correlation function in which the averaging is over the derivative of the energy distribution function. Using the spectrum of the electromagnetic fluctuations, inverting the fluctuation-dissipation relation one can find the permittivity of the medium.     

Low temperature linear dynamical susceptibility of dipolar spin glasses

The dissipative part of the linear magnetic dynamic susceptibility of dipolar spin glasses is considered. Due to the transition of the system (at enough high concentration of the magnetic dipoles) from a paramagnetic phase to a magnetic dipolar one, an anomalous temperature dependence of the dissipative part of the magnetic susceptibility is found. Some considerations related to the experimental results for LiHo_xY _1?xF₄ are made.     

Probing the fluctuation-dissipation theorem in a Perrin-like experiment

In this Letter, we present a new experimental approach to investigate the effective temperature concept as a generalization of the fluctuation-dissipation theorem (FDT) for nonequilibrium systems. Simultaneous measurements of diffusion coefficient and sedimentation velocity of heavy colloids, embedded in a Laponite clay suspension, are performed with a fluorescence-recovery-based setup. This nonperturbative dual measurement, performed at a single time in a single sample, allows for a direct application of the FDT to the tracer velocity observable. It thus provides a well-defined derivation of the effective temperature in this ageing colloidal gel. For a wide range of concentrations and ageing times, we report no violation of the FDT, with effective temperature agreeing with bath temperature. This result is consistent with recent theoretical predictions on the coupling between the velocity observable and nonequilibrium gels dynamics.     

Cooperative rearrangement regions and dynamical heterogeneities in colloidal glasses with attractive versus repulsive interactions

Water-lutidine mixtures permit the interparticle potentials of colloidal particles suspended therein to be tuned, in situ, from repulsive to attractive. We employ these systems to directly elucidate the effects of interparticle potential on glass dynamics in experimental samples composed of the same particles at the same packing fractions. Cooperative rearrangement regions (CRRs) and heterogeneous dynamics are observed in both types of glasses. Compared to repulsive glasses, the attractive glass dynamics are found to be heterogeneous over a wider range of time and length scales, and its CRRs involve more particles. Additionally, the CRRs are observed to be stringlike structures in repulsive glasses and compact structures in attractive glasses. Thus, the experiments demonstrate explicitly that glassy dynamics can depend on the sign of the interparticle interaction.     

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.     

Strong universality and algebraic scaling in two-dimensional Ising spin glasses

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but nonzero temperatures and provide numerical evidence that eta approximately equal 0 and nu approximately equal 3.5 in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds, in particular, for the +/- J model, with or without dilutions, and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T = 0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction.     

Off-equilibrium fluctuation-dissipation relation in a spin glass

We report new experimental results obtained on the insulating spin glass CdCr_2-2x In_2x S₄. Our experimental setup allows a quantitative comparison between the thermo-remanent magnetisation and the autocorrelation of spontaneous fluctuations of magnetisation, yielding a complete determination of the fluctuation-dissipation relation. The dynamics can be studied both in the quasi-equilibrium regime, where the fluctuation-dissipation theorem holds, and in the deeply ageing regime. The limit of separation of time-scales, as used in analytical calculations, can be approached by use of a scaling procedure.Received: 2 March 2004, Published online: 9 September 2004PACS: 05.70.Ln Nonequilibrium and irreversible thermodynamics - 75.50.Lk Spin glasses and other random magnets - 07.20.Dt Thermometers - 07.55.Jg Magnetometers for susceptibility, magnetic moment, and magnetization measurementsD. Hérisson: Present address: Department of Engineering Sciences - Division of Solid State Physics, Uppsala University, 751 21 Uppsala, SwedenM. Ocio: deceased 21 December 2003     

On the fluctuation-dissipation theorem in a disordered nonequilibrium system

We present a modified perturbational calculation for a model with quenched disorder in nonequilibrium. A systematic way is proposed to obtain corrections to the usual fluctuation-dissipation theorem.     

Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. Generalized fluctuation-dissipation theorem

The paper is devoted to the theory of thermal fluctuations in nonlinear macroscopic systems and to the derivation of variational principles of nonlinear nonequilibrium thermodynamics. In the first part of the paper rigorous universal fluctuation-dissipation relations for nonlinear classical and quantum systems, subjected to dynamic as well as thermodynamic perturbations, are derived and analyzed. General expressions for dissipative fluxes and nonlinear transfer coefficients with the help of fluctuation cumulants are found. The canonical structure of nonlinear evolution equations of macrovariables is derived and the rule of introducing langevinian random forces into these equations, in accordance with fluctuation-dissipation relations. A Markovian theory of fluctuations in a stationary nonequilibrium state is constructed.     

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

The [, , ]-Langevin equation describes the time evolution of a real stationary process withT-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [, , ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics.     

A fluctuation-dissipation theorem approach to mechanical relaxation in solid polymers

Abstract

Kubo theory formalism has been used to obtain expressions for shear and dilatational stress relaxation functions in terms of statistical mechanical time-dependent correlation functions. This is equivalent to obtaining expressions for the complex modulus or the complex viscosity for all frequencies. These results provide a basis for calculating the macroscopic consequences of molecular models presently used to provide qualitative understanding of relaxation peaks for solid polymers.

The shear and dilatational stress relaxation functions are quite different formally. For a particularly simple model it will be shown that the former is related to the frequency distribution of the kinetic energy and is also closely related to the dielectric relaxation function. The familiar results of the Rouse model are recovered in the results but no friction constant need be assumed in the present approach.     

A generalization of the fluctuation-dissipation theorem for the case of excess noise

Electrical fluctuations proportional to the square of the external field are investigated in the case of quasi-equilibrium conditions. The binary correlation function, proportional to the square of the external field, is expressed in terms of the zero-field quaternary correlation function for both quantum and classical cases. This result can be considered as a generalization of the fluctuation-dissipation theorem. The 1/f spectrum is obtained as a consequence of the symmetry properties of the quaternary correlation function without consideration of the physical mechanisms responsible for the noise. The method of investigation of the 1/f spectrum through zero-field quaternary correlation function is discussed.     

The fluctuation-dissipation theorem for contracted descriptions of Markov processes

It is shown that if the Onsager-Casimir relations and the fluctuationdissipation theorem are valid for a stationary, Gaussian, Markov process in anN-dimensional space, then these relations are valid when the process is projected into a subspace of the original space. Both time-reversal-even and time-reversal-odd variables are allowed. Previous derivations of the fluctuation-dissipation theorem for Brownian motion from fluctuating hydrodynamics are special cases of the present result. For the Brownian motion problem, the fluctuation-dissipation theorem is proven for the case of a compressible, thermally conducting fluid with a nonlocal equation of state. Arbitrary slip boundary conditions are considered as well.     

Exchange interaction effects in electron spin resonance: Larmor theorem violation in narrow-gap quantum well heterostructures

We report a theoretical study of the exchange interaction effects in the electron spin resonance (ESR) in n-type narrow-gap quantum well (QW) heterostructures. Using the Hartree-Fock approximation, based on the eight-band k?p Hamiltonian, the many-body correction to the ESR energy is found to be nonzero, providing theoretical evidence of Larmor theorem violation in symmetric narrow-gap QWs. We predict the exchange enhancement of the ESR g-factor and its divergence in low magnetic fields. The 'enhanced' ESR g-factor and quasiparticle g-factor, measured in magnetotransport, coincide at even-valued filling factors of the Landau levels in moderate and quantizing magnetic fields.     

Direct imaging of dynamical heterogeneities near the colloid-gel transition

We observe the microscopic dynamics of a suspension of colloids with attractive interaction by confocal fluorescence microscopy to provide a deeper understanding of the relationship between local structure and dynamics near the gel transition. We study the distinct and self-parts of the van Hove density-density correlation function applied to our experimental data. Separable fast and slow populations emerge in the self-part, while the distinct part shows a pronounced signature of dynamic heterogeneities close to the gel transition, dominated by the fast particles. The slow population close to the gel transition shares features with an attraction-driven colloidal glass, including a plateau in the mean squared displacement that provides an estimate for the dynamical localization length.     

A generalization of the fluctuation-dissipation theorem for the case of excess noise

Electrical fluctuations proportional to the square of the external field are investigated in the case of quasiequilibrium conditions. The binary correlation fluctuation proportional to the square of the external field is expressed in terms of the zero-field quaternary correlation function for both quantum and classical cases. This result can be considered as a generalization of the fluctuation-dissipation theorem. As applied to the electrical $\text{1}\text{f}$ noise the novel method investigation both in theory and in experiment is presented. The frequency dependence of zero-field quaternary potential correlation function is suggested to be investigated instead of binary correlation function proportional to the square of external field.