  We derive a two-band finite-dimensional model for description of the
condensate tunneling in an accelerating optical lattice, taking into account
the fine Bloch band structure. The model reveals a very strong dependence of
the final band populations on the initial populations and phases. Most
importantly, additionally to the known asymmetric dependence on the
nonlinearity, there is also a notable asymmetry in the sensitivity of the
tunneling probability to the nonliearity-induced initial population of the
Bloch band to which the tunneling takes place. This fact can explain the
experimentally observed unexpected independence of the upper-to-lower tunneling
probablity on the nonlinearity. Finally, we compare the predictions of the
two-band model with that of the well-known nonlinear Landau-Zener model and
find disagreement when the two bands are initially populated. The disagreement
can be qualitative and reveals itself even for a negligible nonlinearity.
However, the two models agree remarkably well if just one band is populated
initially.
