  Recent experimental realizations of artificial gauge fields for cold atoms
are promising for generating steady states carrying a mass current in strongly
correlated systems, such as the Bose-Hubbard model. Moreover, a homogeneous
condensate confined by hard-wall potentials from laser sheets has been
demonstrated, which provides opportunities for probing the intrinsic transport
properties of isolated quantum systems. Using the time-dependent Density Matrix
Renormalization Group (TDMRG), we analyze the effect of the lattice and
interaction strength on the current generated by a quench in the artificial
vector potential when the density varies from low values (continuum limit) up
to integer filling in the Mott-insulator regime. There is no observable mass
current deep in the Mott-insulator state as one may expect. Other observable
quantities used to characterize the quasi-steady state in the bulk of the
system are the Drude weight and entanglement entropy production rate. The
latter in particular provides a striking signature of the superfluid-Mott
insulator transition. Furthermore, an interesting property of the superfluid
state is the formation of shock and rarefaction waves at the boundaries due to
the hard-wall confining potentials. We provide results for the height and the
speed of the shock front that propagates from the boundary toward the center of
the lattice. Our results should be verifiable with current experimental
capabilities.
