Bosons in a lattice: Exciton-phonon condensate in Cu2O

We explore a nonlinear field model to describe the interplay between the ab ility of excitons to be Bose-condensed and their interaction with other mod es of a crystal.:We apply our consideration to the long-living paraexcitons in Cu2O. Taking into account the exciton-phonon interaction and introducin g a coherent phonon part of the moving condensate, we derive the dynamic-eq uations for the exciton-phonon condensate. These equations can support loca lized solutions, and we discuss the:conditions for the moving inhomogeneous condensate to appear in the crystal. We calculate the condensate wave func tion and energy, and a collective excitation spectrum in the semiclassical approximation; the inside :excitations were found to follow the asymptotic behavior of the macroscopic wave function:exactly.: The stability condition s of the moving condensate are analyzed by use of Landau arguments, and Lan dau critical parameters appear in the theory. Finally, we-apply our model t o describe the recently observed interference rind strong nonlinear interac tion between two coherent exciton-phonon packets in Cu2O.