Quasiequilibrium Mixture of Itinerant and Localized Bose Atoms in   Optical Lattice
  Conditions are studied under which there can exist a quasiequilibrium mixture of itinerant and localized bosonic atoms in an optical lattice, even at zero temperature and at integer filling factor, when such a coexistence is impossible for an equilibrium lattice. The consideration is based on a model having the structure of a two-band, or two-component, boson Hubbard Hamiltonian. The minimal value for the ratio of on-site repulsion to tunneling parameter, necessary for the occurrence of such a mixture, is found. 
V.I. Yukalov, A. Rakhimov, and S. Mardonov
cond-mat.quant-gas quant-ph