arXiv subjects
Publications and source records attributed to Jorge Kurchan.
We discuss a theoretical approach to structural glasses as they happen in real situations. Older ideas based on `configurational entropy', on `fictive temperatures' and on Edwards' `compactivity' are sharpened and unified in an out of equilibrium context. The picture is such that it may be supported or disproved by an experimental test, which we describe.
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs to cast them in a form involving states with finite lifetimes. Starting from elementary examples and using results of Gaveau and Schulman, we propose a simple expression for the configurational entropy and revisit the question of taking flat averages over metastable states. The construction is applicable to finite dimensional systems, and we explicitly show that for simple mean-field glass models it recovers, justifies and generalises the known results. The calculation emphasises the appearance of new dynamical order parameters.
We investigate the dynamics of spin glasses from the `rheological' point of view, in which aging is suppressed by the action of small, non-conservative forces. The different features can be expressed in terms of the scaling of relaxation times with the magnitude of the driving force, which plays the role of the critical parameter. Stated in these terms, ultrametricity loses much of its mystery and can be checked rather easily. This approach also seems a natural starting point to investigate what would be the real-space structures underlying the hierarchy of time scales. We study in detail the appearance of this many-scale behavior in a mean-field model, in which dynamic ultrametricity is clearly present. A similar analysis is performed on numerical results obtained for a 3D spin glass: In that case, our results are compatible with either that dynamic ultrametricity is absent or that it develops so slowly that even in experimental time-windows it is still hardly observable.
We investigate a general scenario for ``glassy'' or ``jammed'' systems driven by an external, non-conservative force, analogous to a shear force in a fluid. In this scenario, the drive results in the suppression of the usual aging process, and the correlation and response functions become time translation invariant. The relaxation time and the response functions are then dependent on the intensity of the drive and on temperature. We investigate this dependence within the framework of a dynamical closure approximation that becomes exact for disordered, fully-connected models. The relaxation time is shown to be a decreasing function of the drive (``shear thinning'' effect). The correlation functions below the glass transition temperature (Tc) display a two time scales relaxation pattern, similar to that observed at equilibrium slightly above Tc. We also study the violation of the fluctuation dissipation relationship in the driven system. This violation is very reminiscent of the one that takes place in a system aging below Tc at zero drive. It involves in particular the appearance of a two-temperatures regime, in the sense of an effective fluctuation dissipation temperature. Although our results are in principle limited to the closure relations that hold for mean-field models, we argue that a number of the salient features are not inherent to the approximation scheme, and may be tested in experiments and simulations.
We present a scenario for the nonequilibrium dynamics in the limit of small entropy production. We discuss (i) the appearence of different time-scales, (ii) the modification of the fluctuation-dissipation theorem and its relation to effective temperatures and partial equilibrations and (iii) the validity of Onsager reciprocity relations. We distinguish these properties by their reaction to infinitesimal perturbations. We recall that one can easily change the time dependence of observables by applying an infinitesimal force while time-reparametrization invariant features remain unchanged under the same perturbations. With the aim of better understanding these properties, we consider the effect of several baths with different temperatures and time-scales on the dynamics. This is done in two ways: numerically, by using a especially developed Monte Carlo algorithm that mimics the coupling to multiple baths; analytically, by computing the time-dependent probability density of simple systems in contact with multiple baths. We finally argue that these features are related to supersymmetry, the reparametrization invariance of the slow dynamics and its spontaneous breaking. This scenario is consistent within any perturbative scheme. A brief version of this article appeared in Physica A263, 242 (1999).
A scenario for systems with slow dynamics is characterised by stating that there are several temperatures coexisting in the sample, with a single temperature shared by all observables at each (widely separate) time-scale. In preparation for the study of granular rheology, we show within this framework that glassy systems with driving and friction that are generic and do not correspond to a thermal bath --- and whose microscopic `fast' motion is hence not thermal --- have a well-defined macroscopic temperature associated to the slow degrees of freedom. This temperature is what a thermometer coupled to the system will measure if tuned to respond to low frequencies, and since it can be related to the number of stationary configurations, it is the formalisation of Edwards' `compactivity' ideas.
We propose an indirect way of studying the fluctuation-dissipation relation in spin-glasses that only uses available susceptibility data. It is based on a dynamic extension of the Parisi-Toulouse approximation and a Curie-Weiss treatment of the average magnetic couplings. We present the results of the analysis of several sets of experimental data obtained from various samples.
We study analytically the effect of temperature cyclings in mean-field spin-glasses. In accordance with real experiments, we obtain a strong reinitialization of the dynamics on decreasing the temperature combined with memory effects when the original high temperature is restored. The same calculation applied to mean-field models of structural glasses shows no such reinitialization, again in accordance with experiments. In this context, we derive some relations between experimentally accessible quantities and propose new experimental protocols. Finally, we briefly discuss the effect of field cyclings during isothermal aging.
The response function of domain growth processes, and in particular the violation of the fluctuation-dissipation theorem, are studied both analytically and numerically. In the asymptotic limit of large times, the fluctuation-dissipation ratio $X$, which quantifies this violation, tends to one if $C>m^2$ and to zero if $C 2$, and as $\ln (L(t))/L(t)$ for $d=2$. Numerical results confirming this analysis are presented.
Recent analytical developments in glass theory are equally relevant to the understanding of anomalous rheology, with characteristic features such as the Reynolds dilatancy and the driving-power dependence of the viscosity arising naturally. A notion of effective temperature based on the fluctuation-dissipation relation can be introduced in the limit of small driving power. Within mean-field, the analogue of the Edwards compactivity can be computed, and it coincides with this effective temperature. The approach does not invoke any particular geometry for the constituents of the fluid, provided it has glassy behaviour.
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.
The fluctuation theorem of Gallavotti and Cohen holds for finite systems undergoing Langevin dynamics. In such a context all non-trivial ergodic theory issues are by-passed, and the theorem takes a particularly simple form. As a particular case, we obtain a nonlinear fluctuation-dissipation theorem valid for equilibrium systems perturbed by arbitrarily strong fields.
We show that for stochastic dynamical systems out of equilibrium the violation of the fluctuation-dissipation equality is bounded by a function of the entropy production. The result applies to a much wider situation than `near equilibrium', comprising diffusion as well as glasses and other macroscopic systems far from equilibrium. For aging systems this bounds the age-frequency regimes in which the susceptibilities satisfy FDT in terms of the rate of decay of the H-function, a question intimately related to the reading of a thermometer placed in contact with the system.
We investigate the aging behavior of lattice-gas models with constrained dynamics in which particle exchange with a reservoir is allowed. Such models provide a particularly simple interpretation of aging phenomena as a slow approach to criticality. They appear as the simplest three dimensional models exhibiting a glassy behavior similar to that of mean field (low temperature mode-coupling) models.
We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i) Phenomenological models of aging (coarsening, trap models), (ii) Analytical results for the low-temperature dynamics of mean-field models (corresponding to the mode-coupling equations); and (iii) Simple non-disordered models with glassy dynamics. We discuss the interrelation between these approaches, and also with previous work in the field. Several open problems are underlined -- in particular the precise relation between mean-field like (or mode-coupling) descriptions and finite dimensional problems.
The low-temperature generalization of the mode-coupling equations corresponds to the dynamics of mean-field disordered models in the glassy phase. The system never achieves equilibrium, preserving the memory of the time elapsed after the quench throughout its evolution. A concept of effective temperature can be made quite rigorous in this context by considering readings of thermometers in different time-scales and the thermalization of weakly coupled subsystems.
We show that, in nonequilibrium systems with small heat flows, there is a time-scale dependent effective temperature which plays the same role as the thermodynamical temperature, in that it controls the direction of heat flows and acts as a criterion for thermalization. We simultaneously treat the case of stationary systems with weak stirring and of glassy systems that age after cooling and show that they exhibit very similar behavior provided that time dependences are expressed in terms of the correlations of the system. We substantiate our claims with examples taken from solvable models with non-trivial low-temperature dynamics, but argue that they have a much wider range of validity. We suggest experimental checks of these ideas.
We show that a family of disordered systems with non-relaxational dynamics may exhibit ``glassy'' behavior at nonzero temperature, although such a behavior appears to be ruled out by a face-value application of mean-field theory. Nevertheless, the roots of this behavior can be understood within mean-field theory itself, properly interpreted. Finite systems belonging to this family have a dynamical regime with a self-similar pattern of alternating periods of fast motion and trapping.