Trap models with slowly decorrelating observables

We study the correlation and response dynamics of trap models of glassy dynamics, considering observables that only partially decorrelate with every jump. This is inspired by recent work on a microscopic realization of such models, which found strikingly simple linear out-of-equilibrium fluctuation-dissipation relations in the limit of slow decorrelation. For the Barrat-Mezard model with its entropic barriers we obtain exact results at zero temperature $T$ for arbitrary decorrelation factor $\kappa$. These are then extended to nonzero $T$, where the qualitative scaling behaviour and all scaling exponents can still be found analytically. Unexpectedly, the choice of transition rates (Glauber versus Metropolis) affects not just prefactors but also some exponents. In the limit of slow decorrelation even complete scaling functions are accessible in closed form. The results show that slowly decorrelating observables detect persistently slow out-of-equilibrium dynamics, as opposed to intermittent behaviour punctuated by excursions into fast, effectively equilibrated states.Comment: 29 pages, IOP styl

Linear and non linear response in the aging regime of the 1D trap model

We investigate the behaviour of the response function in the one dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time tw+t given that a small bias h is applied at time tw. Several scaling regimes are found, depending on the relative values of t, tw and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation dissipation relation is, in this case, valid even in the aging regime.Comment: 5 pages, 3 figures, 3 references adde

The Kovacs effect in model glasses

We discuss the `memory effect' discovered in the 60's by Kovacs in temperature shift experiments on glassy polymers, where the volume (or energy) displays a non monotonous time behaviour. This effect is generic and is observed on a variety of different glassy systems (including granular materials). The aim of this paper is to discuss whether some microscopic information can be extracted from a quantitative analysis of the `Kovacs hump'. We study analytically two families of theoretical models: domain growth and traps, for which detailed predictions of the shape of the hump can be obtained. Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its description requires to deal not only with averages but with a full probability distribution (of domain sizes or of relaxation times). We end by some suggestions for a quantitative analysis of experimental results.Comment: 17 pages, 6 figures; revised versio

On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses

We reformulate the interpretation of the mean-field glass transition scenario for finite dimensional systems, proposed by Wolynes and collaborators. This allows us to establish clearly a temperature dependent length xi* above which the mean-field glass transition picture has to be modified. We argue in favor of the mosaic state introduced by Wolynes and collaborators, which leads to the Adam-Gibbs relation between the viscosity and configurational entropy of glass forming liquids. Our argument is a mixture of thermodynamics and kinetics, partly inspired by the Random Energy Model: small clusters of particles are thermodynamically frozen in low energy states, whereas large clusters are kinetically frozen by large activation energies. The relevant relaxation time is that of the smallest `liquid' clusters. Some physical consequences are discussed.Comment: 8 page

From laser cooling to aging: a unified Levy flight description

Intriguing phenomena such as subrecoil laser cooling of atoms, or aging phenomenon in glasses, have in common that the systems considered do not reach a steady-state during the experiments, although the experimental time scales are very large compared to the microscopic ones. We revisit some standard models describing these phenomena, and reformulate them in a unified framework in terms of lifetimes of the microscopic states of the system. A universal dynamical mechanism emerges, leading to a generic time-dependent distribution of lifetimes, independently of the physical situation considered.Comment: 8 pages, 2 figures; accepted for publication in American Journal of Physic

Evidence for unidimensional low-energy excitations as the origin of persistent spin dynamics in geometrically frustrated magnets

We report specific heat, magnetic, and muon spin relaxation measurements performed on a polycrystalline sample of the normal spinel CdHo2S4. The rare-earth ions sit on a lattice of corner-sharing regular tetrahedra as in pyrochlore compounds. Magnetic ordering is detected at Tc ~ 0.87 K. From spin-lattice relaxation rate measurements on both sides of Tc we uncover similar magnetic excitation modes driving the so-called persistent spin dynamics at T < Tc. Unidimensional excitations are argued to be at its origin. Often observed spin loop structures are suggested to support these excitations. The possibility of a generic mechanism for their existence is discussed.Comment: 7 pages, 8 figure

Fluctuation-dissipation relations in trap models

Trap models are intuitively appealing and often solvable models of glassy dynamics. In particular, they have been used to study aging and the resulting out-of-equilibrium fluctuation-dissipation relations between correlations and response functions. In this note I show briefly that one such relation, first given by Bouchaud and Dean, is valid for a general class of mean-field trap models: it relies only on the way a perturbation affects the transition rates, but is independent of the distribution of trap depths and the form of the unperturbed transition rates, and holds for all observables that are uncorrelated with the energy. The model with Glauber dynamics and an exponential distribution of trap depths, as considered by Barrat and Mezard, does not fall into this class if the perturbation is introduced in the standard way by shifting all trap energies. I show that a similar relation between response and correlation nevertheless holds for the out-of-equilibrium dynamics at low temperatures. The results point to intriguing parallels between trap models with energetic and entropic barriers.Comment: Extended introduction and discussion of relation to results of cond-mat/0303445. 13 pages, 2 figures, IOP styl

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

The evolution of field early-type galaxies to z~0.7

We have measured the Fundamental Plane (FP) parameters for a sample of 30 field early-type galaxies (E/S0) in the redshift range 0.1<z<0.66. We find that: i) the FP is defined and tight out to the highest redshift bin; ii) the intercept \gamma evolves as d\gamma/dz=0.58+0.09-0.13 (for \Omega=0.3, \Omega_{\Lambda}=0.7), or, in terms of average effective mass to light ratio, as d\log(M/L_B)/dz=-0.72+0.11-0.16, i.e. faster than is observed for cluster E/S0 -0.49+-0.05. In addition, we detect [OII] emission >5\AA in 22% of an enlarged sample of 42 massive E/S0 in the range 0.1<z<0.73, in contrast with the quiescent population observed in clusters at similar z. We interpret these findings as evidence that a significant fraction of massive field E/S0 experiences secondary episodes of star-formation at z<1.Comment: ApJ Letters, in pres