Nonlinearity induced destruction of resonant tunneling in the   Wannier-Stark problem
  We present detailed numerical results on the dynamics of a Bose-Einstein condensate in a tilted periodic optical lattice over many Bloch periods. We show that an increasing atom-atom interaction systematically affects coherent tunneling, and eventually destroys the resonant tunneling peaks. 
Sandro Wimberger, Riccardo Mannella, Oliver Morsch, Ennio Arimondo,   Andrey Kolovsky, and Andreas Buchleitner