Related papers: Universal Scaling Laws for Large Events in Driven …
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk…
There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of…
Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the…
Interacting random matrix systems are fundamental to modern theoretical physics and data science, yet a unified framework for their analysis has been lacking. This work introduces such a universal framework, built upon two novel concepts:…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
Recent progress in out-of-equilibrium closed quantum systems has significantly advanced the understanding of mechanisms behind their evolution towards thermalization. Notably, the concept of non-thermal fixed points (NTFPs) - responsible…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model…
Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether…
In this study we are testing whether the power law slopes ($\alpha_F$, $\alpha_E$) of fluxes $(F)$, fluences or energies $(E)$ are universal in their size distributions, $N(F) \propto F^{-\alpha_F}$ and $N(E) \propto E^{-\alpha_E}$, in…
Motivated by the phenomenologies of dynamic roughening of strings in random media and magnetohydrodynamics, we examine the universal properties of driven diffusive system with coupled fields. We demonstrate that cross-correlations between…
Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…
Fusion rules in turbulence specify the analytic structure of many-point correlation functions of the turbulent field when a group of coordinates coalesce. We show that the existence of flux equilibrium in fully developed turbulent systems…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
We consider global quantum quenches, a protocol when a continuous field theoretic system in the ground state is driven by a homogeneous time-dependent external interaction. When the typical inverse time scale of the interaction is much…
A previous scaling analysis of pressure experiments in heavy fermion is reviewed and enlarged. We show that the critical exponents obtained from this analysis indicate that a one-parameter scaling describes these experiments. We obtain…
Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical…
Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the…