Related papers: Dynamical Freezing in a Spin Glass System with Log…
We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global…
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy…
We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…
We use Monte Carlo simulations to study the static and dynamical properties of a Potts glass with infinite range Gaussian distributed exchange interactions for a broad range of temperature and system size up to N=2560 spins. The results are…
We study the extremal process associated with the Discrete Gaussian Free Field on the square lattice and elucidate how the conformal symmetries manifest themselves in the scaling limit. Specifically, we prove that the joint process of…
Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic…
We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, $\beta$--corners…
We use a non-equilibrium simulation method to study the spin glass transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity $v$ (temperature change versus time) in Monte Carlo…
The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity…
We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are…
We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…
Analysis of temperature dependence of structural relaxation time in supercooled liquids revealed a qualitatively distinct feature - a sharp, cusp-like maxumum in the second derivative of its logarithm. It suggests that the super-Arrhenius…
A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb{R}^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $mu$…
The dynamical behavior of a kind of models with hierarchically constrained dynamics is investigated. The models exhibit many properties resembling real structural glasses. In particular, we focus on the study of time-dependent temperature…
We consider quantum rotors or Ising spins in a transverse field on a $d$-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors,…
We numerically study finite-dimensional spin glasses at low and zero temperature, finding evidences for (i) strong time/space heterogeneities, (ii) spontaneous time scale separation and (iii) power law distributions of flipping times. Using…
We have considered the dynamical evolution of cellular patterns controlled by a stochastic Glauber process determined by the deviations of local cell topology from that of a crystalline structure. Above a critical temperature evolution is…
Using quantum parallelism on random walks as original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers -- with internal degrees of freedom which serve as…