Instability of Holographic Superfuids in Optical Lattice

The instability of superfluids in optical lattice has been investigated using the holographic model. The static and steady flow solutions are numerically obtained from the static equations of motion and the solutions are described as Bloch waves with different Bloch wave vector $k$. Based on these Bloch waves, the instability is investigated at two levels. At the linear perturbation level, we show that there is a critical $k_{c}$ above which the superflow is unstable. At the fully nonlinear level, the intermediate state and final state of unstable superflow are identified through numerical simulation of the full equations of motion. The results show that during the time evolution, the unstable superflow will undergo a chaotic state, where solitons will appear and disappear. The system will settle down to a stable state with $k<k_{c}$ eventually, with a smaller current and a larger condensate.