Landau and dynamical instabilities of the superflow of Bose-Einstein condensates in optical lattices

The superfluidity of Bose-Einstein condensates (BECs) in optical lattices is investigated. Apart from the usual Landau instability, which occurs when a BEC flows faster than the speed of sound, the BEC can also suffer a dynamical instability, resulting in period doubling and other sorts of symmetry breaking of the system. Such an instability plays a crucial role in the dissipative motion of a trapped BEC in an optical lattice recently observed.