Related papers: Finite-size fluctuations for stochastic coupled os…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
Recent works have derived and proven the large-population mean-field limit for several classes of particle-based stochastic reaction-diffusion (PBSRD) models. These limits correspond to systems of partial integral-differential equations…
Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two…
We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this…
The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
An effective model is introduced to illustrate finite volume effects beyond the usual momentum space constraints. The fluctuations of the chiral order parameter and the net baryon number, as well as their scaling properties, are…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
A linear open quantum system consisting of a harmonic oscillator linearly coupled to an infinite set of independent harmonic oscillators is considered; these oscillators have a general spectral density function and are initially in a…
In this work, we obtain the central limit theorem for fluctuations of Young diagrams around their limit shape in the bulk of the "spectrum" of partitions of a large integer n (under the Plancherel measure). More specifically, we show that,…
Large fluctuations have received considerable attention as they encode information on the fine-scale dynamics. Large deviation relations known as fluctuation theorems also capture crucial nonequilibrium thermodynamical properties. Here we…
We show that hyperscaling and finite-size scaling imply that the probability distribution of the order parameter in finite size critical systems exhibit data collapse. We consider the examples of equilibrium critical systems, and a…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
Damping on an object generally depends on its conformation (shape size etc.). We consider the Langevin dynamics of a model system with a conformation dependent damping and generalize the fluctuation dissipation relation to fit in such a…
We experimentally investigate the effects of finite-system size on the dynamics of weakly nonlinear random gravity-capillary surface waves. Experiments are conducted in rectangular tanks with varying aspect ratios, in which the fluid…
When an isolated quantum system is driven out of equilibrium, expectation values of general observables start oscillating in time. This article reviews the general theory of such temporal fluctuations. We first survey some results on the…
Over the last half century the liquid-gas phase transition and the magnetization phase transition have come to be well understood. After an order parameter, $r$, is defined, it can be derived how $r=0$ for $T>T_c$ and how $r \propto (T_c -…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…