The Fibonacci family of dynamical universality classes

We use the universal nonlinear fluctuating hydrodynamics approach to study anomalous one-dimensional transport far from thermal equilibrium in terms of the dynamical structure function [1]. Generically for more than one conservation law mode coupling theory is shown to predict a discrete family of dynamical universality classes with dynamical exponents which are consecutive ratios of neighboring Fibonacci numbers, starting with z = 2 (corresponding to a diffusive mode) or z = 3/2 (Kardar-Parisi-Zhang (KPZ) mode). If neither a diffusive nor a KPZ mode √ are present, all Fibonacci modes have as dynamical exponent the golden mean z = (1 + 5)/2. The scaling functions of the Fibonacci modes are asymmetric Levy distributions which are completely fixed by the macroscopic current-density relation and compressibility matrix of the system. The theoretical predictions are confirmed by Monte-Carlo simulations of a three-lane asymmetric simple exclusion process.

[1] V. Popkov, A. Schadschneider J. Schmidt, and G. M. Schutz, PNAS Early Edition

(2015),www.pnas.org/cgi/doi/10.1073/pnas.1512261112