  We describe theoretical models for the recent experimental observation of
Macroscopic Quantum Self-Trapping (MQST) in the transverse dynamics of an
ultracold bosonic gas in a 2D lattice. The pure mean-field model based on the
solution of coupled nonlinear equations fails to reproduce the experimental
observations. It greatly overestimates the initial expansion rates at short
times and predicts a slower expansion rate of the cloud at longer times. It
also predicts the formation of a hole surrounded by a steep square fort-like
barrier which was not observed in the experiment. An improved theoretical
description based on a simplified Truncated Wigner Approximation (TWA), which
adds phase and number fluctuations in the initial conditions, pushes the
theoretical results closer to the experimental observations but fails to
quantitatively reproduce them. An explanation of the delayed expansion as a
consequence of a new type of self-trapping mechanism, where quantum
correlations suppress tunneling even when there are no density gradients, is
discussed and supported by numerical time-dependent Density Matrix
Renormalization Group (t-DMRG) calculations performed in a simplified two
coupled tubes set-up.
