We present our experimental investigations on the subject of
nonlinearity-modified Bloch-oscillations and of nonlinear Landau-Zener
tunneling between two energy bands in a rubidium Bose Einstein condensate in an
accelerated periodic potential. Nonlinearity introduces an asymmetry in
Landau-Zener tunneling. We also present measurements of resonantly enhanced
tunneling between the Wannier-Stark energy levels for Bose-Einstein condensates
loaded into an optical lattice.Comment: Chapter of "Nonlinearities of Periodic Structures and Metamaterials"
(edited by C. Denz, S. Flach, and Yu. Kivshar) to be published by Springe
