On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics

TL;DR

This paper introduces a lattice gas model that naturally exhibits a range of universality classes in nonlinear fluctuating hydrodynamics, including the elusive modified KPZ class, characterized by Fibonacci-based dynamical exponents.

Contribution

The paper identifies a Fibonacci family of universality classes in nonlinear fluctuating hydrodynamics and proposes a lattice gas model that naturally exhibits these classes without fine tuning.

Findings

The universality classes are characterized by Fibonacci ratios of dynamical exponents.

The model includes known classes like diffusion and KPZ as special cases.

Criteria for macroscopic currents to produce other universality classes are derived.

Abstract

We present a lattice gas model that without fine tuning of parameters is expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ) universality class. To this end, we review briefly how non-linear fluctuating hydrodynamics in one dimension predicts that all dynamical universality classes in its range of applicability belong to an infinite discrete family which we call Fibonacci family since their dynamical exponents are the Kepler ratios $z_i = F_{i+1}/F_{i}$ of neighbouring Fibonacci numbers $F_i$, including diffusion ($z_2=2$), KPZ ($z_3=3/2$), and the limiting ratio which is the golden mean $z_\infty=(1+\sqrt{5})/2$. Then we revisit the case of two conservation laws to which the modified KPZ model belongs. We also derive criteria on the macroscopic currents to lead to other non-KPZ universality classes.