Related papers: Hierarchical Diffusion, Aging and Multifractality
Monte Carlo simulations on the SK model have been done to investigate aging processes after a rapid quench from $T=\infty$ to the spin-glass phase. The time range of simulations is taken care of so that the system does not surmount…
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze…
For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to…
For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return…
The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears.…
Most materials age, and their properties change over time. The aging of materials is reflected in their mechanical responses to external stress and strain, which exhibit logarithmic relaxation and universal power-law creep. Those responses…
A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact…
We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in four dimensions under the influence of a non-hamiltonian perturbation. We find that for small asymmetry the model behaves as the hamiltonian one, while for large…
We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
Unexpected relations between fidelity decay and cross form--factor, i.e., parametric level correlations in the time domain are found both by a heuristic argument and by comparing exact results, using supersymmetry techniques, in the…
Logarithmic aging phenomena are prevalent in various systems, including electronic materials and biological structures. This study utilizes a generalized continuous time random walk (CTRW) framework to investigate the mechanisms behind the…
We study the two band degenerate Hubbard model using the Fluctuation Exchange approximation (FLEX) method and compare the results with Quantum Monte-Carlo calculations. Both the self-consistent and the non-self-consistent versions of the…
Applying the new tools developed in [G1], we investigate the arcsine aging regime of the random hopping time dynamics of the REM. Our results are optimal in several ways. They cover the full time-scale and temperature domain where this…
Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
Interacting systems consisting of two rotators and a point mass near a hyperbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of quasi periodic…
We present an analytical approach to the out of equilibrium dynamics of a class of kinetic lattice gases under gravity. The location of the jamming transition, the critical exponents, and the scaling functions characterizing the relaxation…