Studies of the interaction of a Bose-Einstein condensate of two-dimensional spatially indirect excitons with the static fields of impurities, surface acoustic waves, and elementary excitations of a degenerate electron gas have been reviewed. The effects of screening of charged impurities and absorption of a Bleustein-Gulyaev surface acoustic wave by an exciton condensate have been considered. Friedel oscillations of the exciton density in a hybrid electron-exciton system, which consists of spatially separated layers of condensed exciton gas and degenerate electron gas, have been studied. The lifetimes of quasiparticle excitations (electrons, plasmons, and bogolons) in the hybrid system have been calculated. The contributions to the effects under study from condensate and above-condensate particles have been determined. The properties of an excitonic insulator have been analyzed within the Bardeen-Cooper-Schrieffer model with a built-in dissipation-free current.
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