Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical   Lattice
  A theory of the non-symmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a set of linearly coupled nonlinear Schr\"{o}dinger equations. The key role of the modulational instability in rendering the inter-band transitions irreversible is highlighted. 
V. V. Konotop, P. G. Kevrekidis, M. Salerno