Aging is a log-Poisson process, not a renewal process (original) (raw)
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Record dynamics: Direct experimental evidence from jammed colloids
EPL (Europhysics Letters), 2016
In a broad class of complex materials a quench leads to a multi-scaled relaxation process known as aging. To explain its commonality and the astounding insensitivity to most microscopic details, record dynamics (RD) posits that a small set of increasingly rare and irreversible events, so called quakes, controls the dynamics. While key predictions of RD are known to concur with a number of experimental and simulational results, its basic assumption on the nature of quake statistics has proven extremely difficult to verify experimentally. The careful distinction of rare ("record") cage-breaking events from in-cage rattle accomplished in previous experiments on jammed colloids, enables us to extract the first direct experimental evidence for the fundamental hypothesis of RD that the rate of quakes decelerates with the inverse of the system age. The resulting description shows the predicted growth of the particle mean square displacement and of a mesoscopic lengthscale with the logarithm of time.
Mesoscopic fluctuations and intermittency in aging dynamics
Europhysics Letters (EPL), 2006
Mesoscopic aging systems are characterized by large intermittent noise fluctuations. In a record dynamics scenario [P. Sibani and J. Dall, Europhys. Lett. 64, 2003] these events, quakes, are treated as a Poisson process with average α ln(1 + t/tw), where t is the observation time, tw is the age and α is a parameter. Assuming for simplicity that quakes constitute the only source of de-correlation, we present a model for the probability density function (PDF) of the configuration autocorrelation function. Beside α, the model has the average quake size 1/q as a parameter. The model autocorrelation PDF has a Gumbel-like shape, which approaches a Gaussian for large t/tw and becomes sharply peaked in the thermodynamic limit. Its average and variance, which are given analytically, depend on t/tw as a power-law and a power-law with a logarithmic correction, respectively. Most predictions are in good agreement with data from the literature and with the simulations of the Edwards-Anderson spin glass carried out as a test. Introduction.-After a rapid quench of an external parameter, e.g. the temperature, many complex materials age, i.e. their properties slowly change with the waiting time, t w , elapsed from the quench. Ever since the initial observations in polymers [1], evidence has accumulated that spin-glasses [2], type II superconductors [3], glasses [4], and soft condensed matter [5], among others, age in similar ways, e.g. : For observation times t ≪ t w physical averages are nearly constant, and autocorrelations and their conjugate linear response functions are connected by an equilibrium-like fluctuation-dissipation theorem (FDT). Conversely, for t ≫ t w they visibly drift and the FDT is violated. As was recently discovered, the drift happens in an intermittent fashion [6, 7], i.e. through rare, large, and spatially heterogeneous rearrangements , which appear as non-Gaussian tails in the probability density function (PDF) of configurational probes such as colloidal particle displacement [8, 9] and correlation [10] or voltage noise fluctuations in glasses [11]. As aging phenomena are similar for a broad class of interactions, we seek a mesoscopic description, and assume that intermittent events, for short quakes, are the main source of de-correlation in non-equilibrium aging. In the framework of record dynamics [12, 13], quakes are irreversible and are triggered by (energy) fluctuations of record magnitude. We show how this leads to a description of the configurational autocorrelation function, more specifically, the dependence of the shape of its PDF on t, t w , the temperature T and the system size N , which resembles observations for colloidal gels [10] spin-glasses and kinetically constrained models [15, 16]. The model PDF is closely approximated by the Gumbel distributions widely
First-passage statistics for aging diffusion in systems with annealed and quenched disorder
Physical Review E, 2014
Aging, the dependence of the dynamics of a physical process on the time t a since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first-passage dynamics. We find that for an aging continuous time random walk process, the scaling exponent of the density of first-passage times changes twice as the aging progresses and reveals an intermediate scaling regime. The first-passage dynamics depends on t a differently for intermediate and strong aging. Similar crossovers are obtained for the first-passage dynamics for a confined and driven particle. Comparison to the motion of an aged particle in the quenched trap model with a bias shows excellent agreement with our analytical findings. Our results demonstrate how first-passage measurements can be used to unravel the age t a of a physical system.
Noise in Complex Systems and Stochastic Dynamics III, 2005
We discuss the close link between intermittent events ('quakes') and extremal noise fluctuations which has been advocated in recent numerical and theoretical work. From the idea that record-breaking noise fluctuations trigger the quakes, an approximate analytical description of non-equilibrium aging as a Poisson process with logarithmic time arguments can be derived. Theoretical predictions for measurable statistical properties of mesoscopic fluctuations are emphasized, and supporting numerical evidence is included from simulations of short-ranged Ising spin-glass models, of the ROM model of vortex dynamics in type II superconductors, and of the Tangled Nature model of biological evolution.
International Journal of Modern Physics B, 1998
The study of phenomena such as capillary displacement in porous media, fracture propagation, and interface dynamics in quenched random media has attracted a great deal of interest in the last few years. This class of problems does not seem to be treatable with the standard theoretical methods, and the only analytical results come from scaling theory or mapping, for some of their properties, to other solvable models. In this paper a recently proposed approach to problems with extremal dynamics in quenched disordered media, named run time statistics ͑RTS͒ or quenched-stochastic transformation, is described in detail. This method allows us to map a quenched dynamics such as invasion percolation onto a stochastic annealed process with cognitive memory. By combining RTS with the fixed scale transformation approach, we develop a general and systematic theoretical method to compute analytically the critical exponents of invasion percolation, with and without trapping, and directed invasion percolation. In addition we can also understand and describe quantitatively the self-organized nature of the process. ͓S1063-651X͑96͒07207-8͔
Theory of extremal dynamics with quenched disorder: Invasion percolation and related models
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1996
The study of phenomena such as capillary displacement in porous media, fracture propagation, and interface dynamics in quenched random media has attracted a great deal of interest in the last few years. This class of problems does not seem to be treatable with the standard theoretical methods, and the only analytical results come from scaling theory or mapping, for some of their properties, to other solvable models. In this paper a recently proposed approach to problems with extremal dynamics in quenched disordered media, named run time statistics ͑RTS͒ or quenched-stochastic transformation, is described in detail. This method allows us to map a quenched dynamics such as invasion percolation onto a stochastic annealed process with cognitive memory. By combining RTS with the fixed scale transformation approach, we develop a general and systematic theoretical method to compute analytically the critical exponents of invasion percolation, with and without trapping, and directed invasion percolation. In addition we can also understand and describe quantitatively the self-organized nature of the process. ͓S1063-651X͑96͒07207-8͔
Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres
2010
We study the nonequilibrium aging dynamics in a system of quasi-hard spheres at large density by means of computer simulations. We find that, after a sudden quench to large density, the relaxation time initially increases exponentially with the age of the system. After a surprisingly large crossover time, the system enters the asymptotic aging regime characterized by a linear increase of the relaxation time with age. In this aging regime, single particle motion is strongly non-Fickian, with a mean-squared displacement increasing subdiffusively, associated to broad, non-Gaussian tails in the distribution of particle displacements. We find that the system ages through temporally intermittent relaxation events, and a detailed finite size analysis of these collective dynamic fluctuations reveals that these events are not spanning the entire system, but remain spatially localized.
The European Physical Journal B, 2007
We study the intermittent behavior of the energy decay and linear magnetic response of a glassy system during isothermal aging after a deep thermal quench using the Edward-Anderson spin glass model as a paradigmatic example. The large intermittent changes in the two observables are found to occur in a correlated fashion and through irreversible bursts, 'quakes', which punctuate reversible and equilibrium-like fluctuations of zero average. The temporal distribution of the quakes it foun to be a Poisson distribution with an average growing logarithmically on time, indicating that the quakes are triggered by record sized fluctuations. As the drift of an aging system is to a good approximation subordinated to the quakes, simple analytical expressions (Sibani et al. Phys Rev B 74, 224407, 2006) are available for the time and age dependence of the average response and average energy. These expressions are shown to capture the time dependencies of the EA simulation results. Finally, we argue that whenever the changes of the linear response function and of its conjugate autocorrelation function follow from the same intermittent events a fluctuation-dissipation-like relation can arise between the two in off-equilibrium aging.
Aging Renewal Theory and Application to Random Walks
Physical Review X, 2014
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process in which successive events are separated by scalefree waiting time periods. Among other ubiquitous long time properties, this process exhibits aging: events counted initially in a time interval [0, t] statistically strongly differ from those observed at later times [ta, ta + t]. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous time random walk. By this we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking. Along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.