451 research outputs found
Linear response in aging glassy systems, intermittency and the Poisson statistics of record fluctuations
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 found 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.Comment: 10 pages, 17 figures. The mproved version now includes a direct
analysis of the intermittent signal. The new title is hopefully more
informative. Accepted for publication in EPJ
Local state space geometry and thermal metastability in complex landscapes: the spin-glass case
A simple geometrical characterization of configuration space neighborhoods of
local energy minima in spin glass landscapes is found by exhaustive search.
Combined with previous Monte Carlo investigations of thermal domain growth, it
allows a discussion of the connection between real and configuration space
descriptions of low temperature relaxational dynamics. We argue that the part
of state-space corresponding to a single growing domain is adequately modeled
by a hierarchically organized set of states and that thermal (meta)stability in
spin glasses is related to the nearly exponential local density of states
present within each trap.Comment: 16 pages, 8 figures, RevTeX, to appear in Physica A The figures have
been improved and the text somewhat shortened. New references have been adde
Extremal noise events, intermittency and Log-Poisson statistics in non-equilibrium aging of complex systems
We review 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.Comment: 12 pages, 9 figures, to appear in the Proceedings of the third SPIE
International Symposium on Fluctuations and Noise, 23-26 May 2005, Austin,
Texa
Coarse-graining complex dynamics: Continuous Time Random Walks vs. Record Dynamics
Continuous Time Random Walks (CTRW) are widely used to coarse-grain the
evolution of systems jumping from a metastable sub-set of their configuration
space, or trap, to another via rare intermittent events. The multi-scaled
behavior typical of complex dynamics is provided by a fat-tailed distribution
of the waiting time between consecutive jumps. We first argue that CTRW are
inadequate to describe macroscopic relaxation processes for three reasons:
macroscopic variables are not self-averaging, memory effects require an
all-knowing observer,and different mechanisms whereby the jumps affect
macroscopic variables all produce identical long time relaxation behaviors.
Hence, CTRW shed no light on the link between microscopic and macroscopic
dynamics. We then highlight how a more recent approach, Record Dynamics (RD)
provides a viable alternative, based on a very different set of physical ideas:
while CTRW make use of a renewal process involving identical traps of infinite
size, RD embodies a dynamical entrenchment into a hierarchy of traps which are
finite in size and possess different degrees of meta-stability. We show in
particular how RD produces the stretched exponential, power-law and logarithmic
relaxation behaviors ubiquitous in complex dynamics, together with the
sub-diffusive time dependence of the Mean Square Displacement characteristic of
single particles moving in a complex environment.Comment: 6 pages. To appear in EP
Aging in Dense Colloids as Diffusion in the Logarithm of Time
The far-from-equilibrium dynamics of glassy systems share important
phenomenological traits. A transition is generally observed from a
time-homogeneous dynamical regime to an aging regime where physical changes
occur intermittently and, on average, at a decreasing rate. It has been
suggested that a global change of the independent time variable to its
logarithm may render the aging dynamics homogeneous: for colloids, this entails
diffusion but on a logarithmic time scale. Our novel analysis of experimental
colloid data confirms that the mean square displacement grows linearly in time
at low densities and shows that it grows linearly in the logarithm of time at
high densities. Correspondingly, pairs of particles initially in close contact
survive as pairs with a probability which decays exponentially in either time
or its logarithm. The form of the Probability Density Function of the
displacements shows that long-ranged spatial correlations are very long-lived
in dense colloids. A phenomenological stochastic model is then introduced which
relies on the growth and collapse of strongly correlated clusters ("dynamic
heterogeneity"), and which reproduces the full spectrum of observed colloidal
behaviors depending on the form assumed for the probability that a cluster
collapses during a Monte Carlo update. In the limit where large clusters
dominate, the collapse rate is ~1/t, implying a homogeneous, log-Poissonian
process that qualitatively reproduces the experimental results for dense
colloids. Finally an analytical toy-model is discussed to elucidate the strong
dependence of the simulation results on the integrability (or lack thereof) of
the cluster collapse probability function.Comment: 6 pages, extensively revised, final version; for related work, see
http://www.physics.emory.edu/faculty/boettcher/ or
http://www.fysik.sdu.dk/staff/staff-vip/pas-personal.htm
Optimization by Record Dynamics
Large dynamical changes in thermalizing glassy systems are triggered by
trajectories crossing record sized barriers, a behavior revealing the presence
of a hierarchical structure in configuration space. The observation is here
turned into a novel local search optimization algorithm dubbed Record Dynamics
Optimization, or RDO. RDO uses the Metropolis rule to accept or reject
candidate solutions depending on the value of a parameter akin to the
temperature, and minimizes the cost function of the problem at hand through
cycles where its `temperature' is raised and subsequently decreased in order to
expediently generate record high (and low) values of the cost function. Below,
RDO is introduced and then tested by searching the ground state of the
Edwards-Anderson spin-glass model, in two and three spatial dimensions. A
popular and highly efficient optimization algorithm, Parallel Tempering (PT) is
applied to the same problem as a benchmark. RDO and PT turn out to produce
solution of similar quality for similar numerical effort, but RDO is simpler to
program and additionally yields geometrical information on the system's
configuration space which is of interest in many applications. In particular,
the effectiveness of RDO strongly indicates the presence of the above mentioned
hierarchically organized configuration space, with metastable regions indexed
by the cost (or energy) of the transition states connecting them.Comment: 14 pages, 12 figure
Log-Poisson statistics and full aging in glassy systems
We argue that Poisson statistics in logarithmic time provides an idealized
description of non-equilibrium configurational rearrangements in aging glassy
systems. The description puts stringent requirements on the geometry of the
metastable attractors visited at age . Analytical implications for the
residence time distributions as a function of and the correlation
functions are derived. These are verified by extensive numerical studies of
short range Ising spin glasses.Comment: v3 (final): 8 pages, 4 figures. Minor change
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