On the Fibonacci universality classes in nonlinear fluctuating\n hydrodynamics

2017/10/25 by Gunter M. Schütz, Schütz, Gunter M. · 1 citation
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1710.09121

Abstract

We present a lattice gas model that without fine tuning of parameters is\nexpected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ)\nuniversality class. To this end, we review briefly how non-linear fluctuating\nhydrodynamics in one dimension predicts that all dynamical universality classes\nin its range of applicability belong to an infinite discrete family which we\ncall Fibonacci family since their dynamical exponents are the Kepler ratios\nz_i = F_i+1/F_i of neighbouring Fibonacci numbers F_i, including\ndiffusion (z₂=2), KPZ (z₃=3/2), and the limiting ratio which is the\ngolden mean z_\∞=(1+\√(5))/2. Then we revisit the case of two\nconservation laws to which the modified KPZ model belongs. We also derive\ncriteria on the macroscopic currents to lead to other non-KPZ universality\nclasses.\n

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