title: 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 [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. 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 [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] 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.
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany; Centro Interdipartimentale per lo Studio di Dinamiche Complesse, Università di Firenze, 50019 Sesto Fiorentino, Italy;
authors.forename: Vladislav
authors.initials: V
authors.lastname: Popkov
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany; as@thp.uni-koeln.de.
authors.forename: Andreas
authors.initials: A
authors.lastname: Schadschneider
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany;
authors.forename: Johannes
authors.initials: J
authors.lastname: Schmidt
authors.affiliation: Theoretical Soft Matter and Biophysics, Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany.
authors.forename: Gunter M
authors.initials: GM
authors.lastname: Schütz
keywords: Golden Mean; driven diffusion; dynamical exponent; nonequilibrium physics; universality