Related papers: Local scale-invariance in disordered systems
We analyze the stochastic scaling laws arising in the invicid limit of the decaying solutions of the Burgers equation. The linear scaling of the velocity structure functions is shown to reflect the domination by shocks of the long-time…
We present a new technique in order to quantify the dynamics of spatially extended systems. Using a test on the existence of unstable periodic orbits, we identify intermediate spatial scales, wherein the dynamics is characterized by maximum…
We study the out of equilibrium dynamics of several models exhibiting aging. We attempt at identifying various types of aging systems using a phase space point of view: we introduce a trial classification, based on the overlap between two…
This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically…
The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…
We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the…
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…
We extend the standard droplet scaling theory for isothermal aging in spin glasses assuming that the effective stiffness constant of droplets as large as extended defects is vanishingly small. A novel dynamical order parameter and the…
The scaling property of level statistics in the quantum Hall regime, i.e. 2D disordered electron systems subject to strong magnetic fields, is analyzed numerically in the light of the random matrix theory. The energy dependences of the…
In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in…
Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on…
The disordering of an initially phase segregated system of finite size, induced by the presence of highly mobile vacancies, is shown to exhibit dynamic scaling in its late stages. A set of characteristic exponents is introduced and computed…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the…
We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the…
Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is…
The localization in a disordered system of $N$ interacting spins coupled by the long-range anisotropic interaction $1/R^{\alpha}$ is investigated using a finite size scaling in a $d=1$ -dimensional system for $N=8, 10, 12, 14$. The results…
Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or…
The dynamical scaling and ageing in the relaxational dynamics of the quenched directed spherical model is analysed. The exact two-time correlation and response functions display new regimes of ballistic or anisotropic ballistic scaling, at…