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 which exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of non-equilibrium universality classes. Remarkably their dynamical exponents \(z_\alpha\) are given by ratios of neighbouring Fibonacci numbers, starting with either \(z_1=3/2\) (if a KPZ mode exist) or \(z_1=2\) (if a diffusive mode is present). If neither a diffusive nor a KPZ mode are present, all dynamical modes have the Golden Mean \(z=(1+\sqrt{5})/2\) as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric L\'evy distributions which are completely fixed by the macroscopic current-density relation and compressibility matrix of the system and hence accessible to experimental measurement.