Dear Colleagues,

Since its introduction in 1960, the concept of universality has been constantly gaining broader usage in many domains of science. Systems usually display universality in a scaling limit, where a certain number of physical observables exhibit identical properties, irrespective of the details of the microscopical dynamics. In the past two decades, universal scaling has prominently emerged as a key feature of physical processes exhibiting anomalous transport. A typical example is the scale-invariant form of the probability density function of the system’s relevant observable or, when such density is unknown or not self-similar, universal features shine through the asymptotic behavior of the density moments in time, or through the scaling expression of the correlation functions. In systems exhibiting glassy or localization transition, anomalous diffusion is accompanied by universal scaling laws, concomitant with a power-law growth of the correlation length. Yet, anomalous transport often characterizes interacting many-particle systems confined to low dimensionality, in the realms of both quantum and classical models, integrable and non-integrable Hamiltonian systems, in and out of equilibrium:  here, universality classes define the divergence of the coefficients of heat conduction, current–current or density–density time correlation functions decay, Green–Kubo relations, as well as spin dynamical correlations in 1D spin systems.       

Importantly, a unique aspect that seems to characterize anomalous transport systems is that universality emerges as a natural element of the passage from the microscopic level to the macroscopic level of description: the infinite many ‘‘degrees of freedom’’ allowed on the microscopic level collapse to few relevant ‘‘degrees of freedom’’ allowed on the macroscopic level. Remarkably, these relevant variables are governed by equations whose mathematical forms appear to be universal.

On the other hand, universality may not to be “that universal”. Different scalings can determine the bulk and the tail of the probability distributions, as well as the time behavior of the correlation functions, depending crucially on the characteristic scales involved. Moreover, the sensitivity of the asymptotic dynamics on the microscopic details observed in some systems leads one to question the bedrock of universality.

This Special Issue aims to provide a collection of the recent progress toward the systematic comprehension of anomalous transport phenomena, through the identification of universal features. In particular, this Special Issue will collect new ideas and describe numerical and analytical methods for the detection and evaluation of universal scalings.

Dr. Alessandro Taloni
Guest Editor

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• universality classes
• anomalous transport
• scaling relations
• fractional equations
• low-dimensional systems
• quantum anomalous transport
• glassy transition
• localization transition
• random walk