Fibonacci family of dynamical universality classes - Kölner UniversitätsPublikationsServer

Popkov, Vladislav ORCID: 0000-0002-8893-3678, Schadschneider, Andreas ORCID: 0000-0002-2054-7973, Schmidt, Johannes and Schuetz, Gunter M. (2015). Fibonacci family of dynamical universality classes. Proc. Natl. Acad. Sci. U. S. A., 112 (41). S. 12645 - 12651. WASHINGTON: NATL ACAD SCIENCES. ISSN 0027-8424

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DOI:10.1073/pnas.1512261112

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 z(alpha) are given by ratios of neighboring Fibonacci numbers, starting with either z(1) = 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 the Golden Mean z = (1+root 5)/2 as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Levy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Popkov, Vladislav	UNSPECIFIED	orcid.org/0000-0002-8893-3678	UNSPECIFIED
Schadschneider, Andreas	UNSPECIFIED	orcid.org/0000-0002-2054-7973	UNSPECIFIED
Schmidt, Johannes	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Schuetz, Gunter M.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED