17-08U

Instabilities resulting in Bose-Einstein condensation and/or modulation of “displacements” in the system of quantum particles described by the two-state Bose-Hubbard model are investigated. A modulation, which doubles the lattice constant, is detected. Conditions for realization of the mentioned instabilities are analyzed, behavior of order parameters is investigated and phase diagrams of the system are calculated both analytically (ground state) and numerically (at non-zero temperatures). It is revealed that the supersolid phase is thermodynamically unstable and does not appear.