Mean-field and stability analysis of two-dimensional flowing soft-core   bosons modeling a supersolid
  The soft-core boson system is one of the simplest models of supersolids, which have both off-diagonal long-range order (Bose-Einstein condensation) and diagonal long-range order (crystalline order). Although this model has been studied from various points of view, studies of the stability of current-flowing states are lacking. Solving the Gross-Pitaevskii and Bogoliubov equations, we obtain excitation spectra in superfluid, supersolid, and stripe phases. On the basis of the results of the excitation spectra, we present a stability phase diagram that shows the region of the metastable superflow states for each phase. 
Masaya Kunimi and Yusuke Kato
cond-mat.quant-gas