Alladi Ramakrishnan Hall

The Fibonacci family of dynamical universality classes

Gunter Schutz

Institute of Complex Systems II Forschungszentrum Jülich GmbH

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. 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+\sqrt5)/2. The scaling functions of the Fibonacci modes are asymmetric Lévy distributions which are completely fixed by the macroscopic stationary properties, viz. the current-density relation and the compressibility matrix of the system. The theoretical predictions are confirmed by Monte-Carlo simulations of a three-lane asymmetric simple exclusion process.