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Dynamical instability in the S=1 Bose-Hubbard model

We study the dynamical instabilities of superfluid flows in the S=1 Bose-Hubbard model. The time evolution of each spin component in a condensate is calculated based on the dynamical Gutzwiller approximation for a wide range of interactions, from a weakly correlated regime to a strongly correlated regime near the Mott-insulator transition. Owing to the spin-dependent interactions, the superfluid flow of the spin-1 condensate decays at a different critical momentum from a spinless case when the interaction strength is the same. We furthermore calculate the dynamical phase diagram of this model and clarify that the obtained phase boundary has very different features depending on whether the average number of particles per site is even or odd. Finally, we analyze the density and spin modulations that appear in association with the dynamical instability. We find that spin modulations are highly sensitive to the presence of a uniform magnetic field.