We explain the experimentally observed instability of cold exciton gases and the formation of a macroscopically ordered exciton state in terms of a thermodynamic model accounting for the phase fluctuations of the condensate. We show that the temperature dependence of the exciton energy exhibits fundamental scaling behavior with the signature of the second order phase transition.

We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form ω ∝ p 2 in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a 3D weakly-interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In 2D the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.PACS numbers: 71.35.Lk arXiv:1712.00039v3 [cond-mat.quant-gas]

We address, theoretically, the puzzling similarity observed in the thermodynamic behavior of independent clouds of cold dipolar excitons in coupled semiconductor quantum wells. We argue that the condensation of self-trapped exciton gas starts at the same critical temperature in all traps due to the specific scaling rule. As a consequence of the reduced dimensionality of the system, the scaling parameters appear to be insensitive to disorder.