Low-acceleration instability of a Bose-Einstein condensate in an optical lattice

We study a Bose-Einstein condensate in a one-dimensional accelerated optical lattice using the mean-field version of the Bose-Hubbard model. Reminiscent of recent experiments [M. Cristiani , Opt. Express 12, 4 (2004)], we find a new type of an instability in this system that occurs in the limit when the acceleration is small.