Fibonacci family of dynamical universality classes

by Vladislav Popkov

Wednesday 16 Dec 2015, 14:30 → 15:30 Europe/Rome

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. % [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)