Related papers: Universal features of fluctuations
We demonstrate the non-universal behavior of finite size scaling in (1+1) dimension of a nonlinear discrete growth model involving extended particles in generalized point of view. In particular, we show the violation of the universal nature…
We study the critical dynamics of a scalar field theory with $Z_2$ symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the…
Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations $C=\beta^{2}<\delta U^{2}>$, which is able to describe the existence of macrostates with negative heat…
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from…
Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems…
A review of the statistical properties of earthquakes is provided, centered mainly in the work of the author (apologies for that). We explain the scaling law for the recurrence-time distributions, its universal character for stationary…
There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping,…
Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…
In this Article we review some recent progresses in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation-dissipation theorem can be derived for Markov processes, and discuss the…
Exerting fluctuations is a part of our daily life: traffic noise, heartbeat, opinion poll, currency exchange rate, electrical current, chemical reactions - they all permanently fluctuate. One of the most important questions is why the…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically. For most concentrations of the scatterers the trajectories close…
The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…