  Motivated by a recent experiment on the non-equilibrium dynamics of
interacting bosons in ladder-shaped optical lattices, we report exact
calculations on the sweep dynamics of Bose-Hubbard systems in finite two-leg
ladders. The sweep changes the energy bias between the legs linearly over a
finite time. As in the experiment, we study the cases of [a] the bosons
initially all in the lower-energy leg (ground state sweep) and [b] the bosons
initially all in the higher-energy leg (inverse sweep). The approach to
adiabaticity in the inverse sweep is intricate, as the transfer of bosons is
non-monotonic as a function of both sweep time and intra-leg tunnel coupling.
Our exact study provides explanations for these non-monotonicities based on
features of the full spectrum, without appealing to concepts (e.g., gapless
excitation spectrum) that are more appropriate for the thermodynamic limit. We
also demonstrate and study Stueckelberg oscillations in the finite-size
ladders.
