Derivation of the two-fluid model for Bose-condensed excitons

Abstract

The second reduced electron-hole density matrix is shown to have the property of off-diagonal long-range order for a Bose-condensed system of Wannier excitons. From the equations of motion for this density matrix the conservation laws for the density, the particle current density, and the energy density of the excitons are derived, as well as the equation of motion for the velocity of the condensate. These equations are obtained by projecting the electron-hole density matrices into the exciton space. From the above-mentioned conservation laws the two-fluid model is deduced, which describes the superfluid flow of excitation energy. In the low-density limit all hydrodynamical quantities are calculated explicitly. Extensions to the case of condensation in the presence of static homogenous electromagnetic fields and to the case of indirect semiconductors are given.