Description
Golden Ratio $\phi=(1+\sqrt{5})/2$, also called Divine Proportion, is the most
perfect irrational number, and it has inspired people for many
centuries.
It is best approximated by the ratios of the two neighbouring integer
numbers from the celebrated Fibonacci sequence 1,1,2,3,5,8,13,21,...,
the so-called Kepler ratios.
We show that dynamical exponents, characterising universal scaling of
space-time fluctuations of the slow
relaxation modes in non-equilibrium systems are all
characterized by the Kepler ratios.
Kepler ratios, i.e. z= 2/1, 3/2, 5/3, 8/5, ...\phi
thus form an infinite discrete family of non-equilibrium
universality classes. First two members of the family are well known,
as diffusion universality z=2 , and Kardar-Parisi-Zhang z=3/2
universality classes.
Our findings are based on mode-coupling theory which predicts also the universal
scaling functions, which are completely fixed by macroscopic
properties of a system. A simple statistical model which allows to see higher
Fibonacci classes z=5/3, z=8/5, and z=\phi, is presented.
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[1] V. Popkov, A. Schadschneider, J. Schmidt, and G.M. Schuetz,
PNAS 112, 12645 (2015)
[2] V. Popkov, J. Schmidt, and G.M. Schuetz,
Phys. Rev. Lett. 112, 200602 (2014)