Wannier-Stark chaos of a Bose-Einstein condensate in 1D optical lattices

Using the idea of the macroscopic quantum wave function and the definition of the Melnikov chaos, we investigate the spatially chaotic features of a Bose-Einstein condensate (BEC) in a Wannier-Stark potential for the trivial phase and the non-trivial phase cases. The perturbed chaotic solutions are constructed, and the chaotic and unstable regions on the parameter space are illustrated. Numerical calculations to the spatial evolutions of the atomic number density and the energy density demonstrate the analytical results and exhibit the chaotic spatial distribution and energy distribution of the BEC atoms.