Fibonacci family of dynamical universality classes

Abstract

Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent z=2, another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with z =3=2. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents zα are given by ratios of neighboring Fibonacci numbers, starting with either z1 = 3=2 (if a KPZ mode exist) or z1 =2 (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have pffiffiffi the Golden Mean z =(1+ √)=2 as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.