相关论文: Aging Random Walks

We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…

Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…

Although species longevity is subject to a diverse range of selective forces, the mortality curves of a wide variety of organisms are rather similar. We argue that aging and its universal characteristics may have evolved by means of a…

The configurational de-correlation in an aging system is attributed to irreversible intermittent rearrangements, which are described as a Poisson process with average $\propto \ln(1 + t/t_w)$, where $t$ is the observation time and $t_w$ is…

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…

In these lecture notes I describe some of the main theoretical ideas emerged to explain the aging dynamics. This is meant to be a very short introduction to aging dynamics and no previous knowledge is assumed. I will go through simple…

Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…

A simple mathematical model of the aging process for long-lived organisms is considered. The key point in this model is the assumption that the body does not have internal clocks that count out the chronological time at scales of decades.…

Aging in complex systems is studied via the sandpile model. Relaxation of avalanches in sandpiles is observed to depend on the time elapsed since the begining of the relaxation. Levy behavior is observed in the distribution of…

We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law…

The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the…

We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…

Disordered materials under an imposed forcing can display creep and aging effects, accompanied by intermittent, spatially heterogeneous dynamics. We propose a unifying microscopic description of these phenomena, based on the notion that as…

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…

We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling…

Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution…

We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and…

In the framework of recently introduced frustrated lattice gas models, we study the out of equilibrium dynamical processes during the compaction process in granular media. We find irreversible-reversible cycles in agreement with recent…

We consider a one-dimensional random walk among biased i.i.d. conductances, in the case where the random walk is transient but sub-ballistic: this occurs when the conductances have a heavy-tail at $+\infty$ or at $0$. We prove that the…

We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…