16 (a) (b) (c) −1 −0.5 0 0.5 1 −0.5 0 0.5 1  /   n/j −1 −0.5 0 0.5 1 −0.5 0 0.5 1  /   n/j −1 −0.5 0 0.5 1 0 0.05 0.1 0.15 0.2  P(n)   n (a) (b) 0 3 6 9 0.9 0.92 0.94 0.96 0.98 1 1.02  S x  t (scaled)  0 2 4 6 8 −1 −0.8 −0.6 −0.4 −0.2 0 0.2  S x  t (scaled)  (c) (d) 0 2 4 6 8 −0.8 −0.2 0.4  S x  t (scaled)  0 3 6 9 0.1 0.2 0.3 0.4 0.5 S x  t (scaled)  FIG. 4: (Color online) The variation of S$_{x}$ ( t ) with time for N =40 particles with u = 5, for Zero (a), Pi (b), Edge (c), and TwinFock (d) preparations. Note the different vertical scale. The dashed-dotted lines are based on semiclassical simulation. Note that the fluctuations of a semiclassical preparation always die after a transient, which should be contrasted with both the classical (single trajectory) and quantum (superposition of M > 1 eigenstates) behavior. FIG. 3: (Color online) The evolving quantum state of N = 40 bosons with u = 5 for TwinFock ( n = 0) preparation. Here and below the units are such that K = 1. The time is t = 4. (a) Wigner function of the evolved quantum state. (b) Semiclassical evolved state. (c) Occupation statistics, with the semiclassical result shown as dashed-dotted line.