  We investigate the dynamics of a wave packet in a parity-breaking
one-dimensional periodic potential slowly varied in time and perturbed by a
linear potential. Parity is broken by considering an asymmetric double well per
unit cell. By comparing the prediction of the semiclassical dynamics with the
full Schr\"odinger solution, we show that Bloch oscillations are strongly
affected by anomalous velocity corrections related to Berry's phase. We
characterize how these effects depend on the degree of parity breaking of the
potential and on the modulation parameters. We also discuss how to measure the
effects of the anomalous velocity in current experiments with non-interacting
Bose-Einstein condensates in bichromatic optical lattices, under the effect of
gravity.
