Title: Weakly nonergodic dynamics in the Gross--Pitaevskii lattice,
Abstract: The microcanonical Gross--Pitaevskii (aka semiclassical Bose-Hubbard) lattice
model dynamics is characterized by a pair of energy and norm densities. The
grand canonical Gibbs distribution fails to describe a part of the density
space, due to the boundedness of its kinetic energy spectrum. We define
Poincare equilibrium manifolds and compute the statistics of microcanonical
excursion times off them. The tails of the distribution functions quantify the
proximity of the many-body dynamics to a weakly-nonergodic phase, which occurs
when the average excursion time is infinite. We find that a crossover to
weakly-nonergodic dynamics takes place inside the nonGibbs phase, being
unnoticed by the largest Lyapunov exponent. In the ergodic part of the
non-Gibbs phase, the Gibbs distribution should be replaced by an unknown
modified one. We relate our findings to the corresponding integrable limit,
close to which the actions are interacting through a short range coupling
network.