Johannes Schmidt

Fibonacci family of dynamical universality classes

Significance Universality is a well-established central concept of equilibrium physics. It asserts that, especially near phase transitions, the properties of a physical system do not depend on its details such as the precise form of interactions. Far from equilibrium, such universality has also been observed, but, in contrast to equilibrium, a deeper understanding of its underlying principles is still lacking. We show that the two best-known examples of nonequilibrium universality classes, the diffusive and Kardar−Parisi−Zhang classes, are only part of an infinite discrete family. The members of this family can be identified by their dynamical exponent, which, surprisingly, can be expressed by a Kepler ratio of Fibonacci numbers. This strongly indicates the existence of a simpler underlying mechanism that determines the different classes. 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 zα are given by ratios of neighboring Fibonacci numbers, starting with either z1=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+5)/2 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.

Defect-induced phase transition in the asymmetric simple exclusion process

We reconsider the long-standing question of the critical defect hopping rate r c in the one-dimensional totally asymmetric exclusion process (TASEP) with a slow bond (defect). For r 0.99 and give strong evidence that indeed as predicted by mean-field theory, and anticipated by recent theoretical findings.

Superdiffusive Modes in Two-Species Driven Diffusive Systems

Using mode coupling theory and dynamical Monte-Carlo simulations we investigate the scaling behaviour of the dynamical structure function of a two-species asymmetric simple exclusion process, consisting of two coupled single-lane asymmetric simple exclusion processes. We demonstrate the appearence of a superdiffusive mode with dynamical exponent

Universality Classes in Two-Component Driven Diffusive Systems

z=5/3

Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension

in the density fluctuations, along with a KPZ mode with

Targeting pure quantum states by strong noncommutative dissipation

z=3/2

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

and argue that this phenomenon is generic for short-ranged driven diffusive systems with more than one conserved density. When the dynamics is symmetric under the interchange of the two lanes a diffusive mode with

Spin-helix states in the XXZ spin chain with strong boundary dissipation

z=2

When is a bottleneck a bottleneck

appears instead of the non-KPZ superdiffusive mode.

Height distribution tails in the Kardar–Parisi–Zhang equation with Brownian initial conditions

We study time-dependent density fluctuations in the stationary state of driven diffusive systems with two conserved densities