Figure 3 : Classical phase locking indicates growth of quantum number fluctuations.

From: Classical synchronization indicates persistent entanglement in isolated quantum systems

Figure 3

(a) The classical synchronization order parameter r measures the degree of locking emerging for K>Kc. (b) Synchronization implies an exponential growth of quantum fluctuations. The maximum growth rate in the limit of large systems becomes proportional to the classical synchronization order parameter r as predicted by equation (11). (c) The average phase velocity in the Kuramoto model as a function of natural frequency . Oscillators in the grey region are phase locked, that is, the average phase velocity is identical. (d) Quantum number fluctuations grow rapidly for the oscillators in the the region of classical phase locking (grey), indicated by non-zero values of the growth rate . Results are shown for globally coupled oscillators, that is, in the limit L→∞. Natural frequencies are drawn from a Lorentzian distribution g(ω), for which r(K)= near Kc=2/(πg(0)) (refs 2, 3). Parameters are U=0 and K=2Kc in c,d.