Memory effects in classical and quantum mean-field disordered models

We apply the Kovacs experimental protocol to classical and quantum p-spin models. We show that these models have memory effects as those observed experimentally in super-cooled polymer melts. We discuss our results in connection to other classical models that capture memory effects. We propose that a similar protocol applied to quantum glassy systems might be useful to understand their dynamics.Comment: 24 pages, 12 figure

A simple system with two temperatures

We study the stationary nonequilibrium regime which settles in when two single-spin paramagnets each in contact with its own thermal bath are coupled. The response vs. correlation plot exhibits some features of aging systems, in particular the existence, in some regimes, of effective temperatures.Comment: 7 pages, 3 figure

Monte-Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes

Numerical simulations of various domain growth systems are reported, in order to compute the parameter describing the violation of fluctuation dissipation theorem (FDT) in aging phenomena. We compute two-times correlation and response functions and find that, as expected from the exact solution of a certain mean-field model (equivalent to the O(N) model in three dimensions, in the limit of N going to infinity), this parameter is equal to one (no violation of FDT) in the quasi-equilibrium regime (short separation of times), and zero in the aging regime.Comment: 5 pages, 5 eps figure

Thermal properties of slow dynamics

The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the Gibbs-Boltzmann distribution, or a small departure from it. Interesting cases in which it is not are glasses, phase-separation, and certain driven complex fluids. We describe a scenario with several coexisting temperatures acting on different timescales, and partial equilibrations at each time scale. This scenario entails strong modifications of the fluctuation-dissipation equalities and the existence of some unexpected reciprocity relations. Both predictions are open to experimental verification, particularly the latter. The construction is consistent in general, since it can be viewed as the breaking of a symmetry down to a residual group. It does not assume the presence of quenched disorder. It can be -- and to a certain extent has been -- tested numerically, while some experiments are on their way. There is furthermore the perspective that analytic arguments may be constructed to prove or disprove its generality.Comment: 11 pages, invited talk to be presented at STATPHYS 20, Pari

Out of equilibrium dynamics of classical and quantum complex systems

Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take very long times. From the point of view of fundamental physics no generic principle such as the ones of thermodynamics allows us to fully understand their behaviour. The alternative is to treat each case separately. It is illusionary to attempt to give, at least at this stage, a complete description of all non-equilibrium situations. Still, one can try to identify and characterise some concrete but still general features of a class of out of equilibrium problems - yet to be identified - and search for a unified description of these. In this report I briefly describe the behaviour and theory of a set of non-equilibrium systems and I try to highlight common features and some general laws that have emerged in recent years.Comment: 36 pages, to be published in Compte Rendus de l'Academie de Sciences, T. Giamarchi e

Effective temperatures out of equilibrium

We describe some interesting effects observed during the evolution of nonequilibrium systems, using domain growth and glassy systems as examples. We breafly discuss the analytical tools that have been recently used to study the dynamics of these systems. We mainly concentrate on one of the results obtained from this study, the violation of the fluctuation-dissipation theorem and we discuss, in particular, its relation to the definition and measurement of effective temperatures out of equilibrium.Comment: 13 pages, RevTex, 2 figs, to appear in ``Trends in Theoretical Physics II'', eds. H Falomir et al, Am. Inst. Phys. Conf. Proc. of the 1998 Buenos Aires meetin

Slow nonequilibrium dynamics: parallels between classical and quantum glasses and gently driven systems

We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas of entropy crisis, fictive temperatures, free-volume... have clear definitions within these models. Aging effects in the glass phase are also captured. One of the salient features of the analytic solution, the breakdown of the fluctuation-dissipation relations, provides a definition of a bonafide {\it effective temperature} that is measurable by a thermometer, controls heat flows, partial equilibrations, and the reaction to the external injection of heat. The effective temperature is an extremely robust concept that appears in non-equilibrium systems in the limit of small entropy production as, for instance, sheared fluids, glasses at low temperatures when quantum fluctuations are relevant, tapped or vibrated granular matter, etc. The emerging scenario is one of partial equilibrations, in which glassy systems arrange their internal degrees of freedom so that the slow ones select their own effective temperatures. It has been proven to be consistent within any perturbative resummation scheme (mode coupling, etc) and it can be challenged by experimental and numerical tests, some of which it has already passed.Comment: 15 pages, 8 figure

Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation

The experimental time scale dependence of thermodynamic relations in out-of-equilibrium systems with aging phenomena is investigated theoretically by using only aging properties of the two-time correlation functions and the generalized fluctuation-dissipation theorem (FDT). We show that there are two experimental time regimes characterized by different thermal properties. In the first regime where the waiting time is much longer than the measurement time, the principle of minimum work holds even though a system is out of equilibrium. In the second regime where both the measurement time and the waiting time are long, the thermal properties are completely different from properties in equilibrium. For the single-correlation-scale systems such as $p$-spin spherical spin-glasses, contrary to a fundamental assumption of thermodynamics, the work done in an infinitely slow operation depends on the path of change of the external field even when the waiting time is infinite. On the other hand, for the multi-correlation-scale systems such as Sherrington-Kirkpatrick model, the work done in an infinitely slow operation is independent of the path. Our results imply that in order to describe thermodynamic properties of systems with aging it is essential to consider the experimental time scales and history of a system as a state variable is necessary.Comment: 28 pages(REVTeX), 4 figure(EPS). To be published in Phys. Rev.

Anomalous diffusion of a particle in an aging medium

We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to $|\omega|^{\delta-1}$ at small frequencies, with $0<\delta<2$. The aging properties of the medium are encoded in a frequency dependent effective temperature $T_{\rm eff.}(\omega)$. The latter is modelized by a function proportional to $|\omega|^\alpha$ at small frequencies, with $\alpha<0$, thus allowing for the medium to have a density of slow modes proportionally larger than in a thermal bath. Using asymptotic Fourier analysis, we obtain the behaviour at large times of the velocity correlation function and of the mean square displacement. As a result, the anomalous diffusion exponent in the aging medium appears to be linked, not only to $\delta$ as it would be the case in a thermal bath, but also to the exponent $\alpha$ characterizing the density of slow modes