On Bose-Einstein condensate inside moving exciton-phonon droplets

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 solve quasi-stationar y equations for the exciton-phonon condensate. These equations support loca lized solutions, and we discuss the conditions for the inhomogeneous conden sate to appear in the crystal. Allowable values of the characteristic width of ballistic condensates are estimated in the limit T --> 0. The stability conditions of the moving condensate are analyzed by use of Landau argument s, and Landau critical parameters appear in the theory. It follows that, un der certain conditions, the condensate can move through the crystal as a st able droplet. To separate the coherent and non-coherent parts of the excito n-phonon packet, we suggest turning off the phonon wind by the changes in d esign of the 3D crystal and boundary conditions for the moving droplet. (C) 2000 Published by Elsevier Science B.V. All rights reserved.