Related papers: Hierarchical Diffusion, Aging and Multifractality
We report new results about the two-time dynamics of an anomalously diffusing classical particle, as described by the generalized Langevin equation with a frequency-dependent noise and the associated friction. The noise is defined by its…
We show that, on a $d-$dimensional hypercubic lattice with $d>1$, conserved-mass transport processes, with {\it multidirectional} hopping that respect all symmetries of the lattice, exhibit power-law correlations for generic parameter…
Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
We study the angular diffusion in a classical $d-$dimensional inertial XY model with interactions decaying with the distance between spins as $r^{-\alpha}$, wiht $\alpha\geqslant 0$. After a very short-time ballistic regime, with…
Super-diffusion, characterized by a spreading rate $t^{1/\alpha}$ of the probability density function $p(x,t) = t^{-1/\alpha} p \left( t^{-1/\alpha} x , 1 \right)$, where $t$ is time, may be modeled by space-fractional diffusion equations…
Random multifractals occur in particular at critical points of disordered systems. For Anderson localization transitions, Mirlin and Evers [PRB 62,7920 (2000)] have proposed the following scenario (a) the Inverse Participation Ratios…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
Aging effects in the two-time correlation function and the response function after a quench from a high temperature to some low temperature are considered for a simple kinetic random energy model exhibiting stretched exponential relaxation.…
We study the dynamics of a system of hard-core particles sliding downwards on a one dimensional fluctuating interface, which in a special case can be mapped to the problem of a passive scalar advected by a Burgers fluid. Driven by the…
We conduct athermal simulations of freely-cooling, viscous soft spheres around the jamming transition density \phi_{J}, and find evidence for a growing length \xi(t) that governs relaxation to mechanical equilibrium. \xi(t) is manifest in…
Using molecular dynamics computer simulations we investigate the aging dynamics of a gel. We start from a fractal structure generated by the DLCA-DEF algorithm, onto which we then impose an interaction potential consisting of a short-range…
In this letter we announce rigorous results on the phenomenon of aging in the Glauber dynamics of the random energy model and their relation to Bouchaud's 'REM-like' trap model. We show that, below the critical temperature, if we consider a…
We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
The time-dependent work probability distribution function $P(W)$ is investigated analytically for a diffusing particle trapped by an anisotropic harmonic potential and driven by a nonconservative drift force in two dimensions. We find that…
Multitime correlation functions provide useful probes for the ensembles of trajectories underlying the stochastic dynamics of complex systems. These can be obtained by measuring their optical response to sequences of ultrashort optical…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…
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',…
Dynamical systems can display a plethora of ergodic and ergodicity breaking behaviors, ranging from simple periodicity to ergodicity and chaos. Here we report an unusual type of non-ergodic behavior in a many-body discrete-time dynamical…
Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…