Stability of Bose-Einstein condensates in two-dimensional optical lattices

Both Landau instability and dynamical instability of Bose-Einstein condensates in moving two-dimensional optical lattices are investigated numerically and analytically. Phase diagrams for both instabilities are obtained numerically for different system parameters. These phase diagrams show that the Landau instability does not depend on direction for weak lattices while the dynamic instability is direction dependent. These features are explained analytically.