| In this thesis, we study the possibility for excitons to form a highly correlated state which can be associated with Bose-Einstein Condensation and has finite extent in space. In particular, we study solitonic mechanisms of exciton superfluidity. We provide a theoretical explanation of recent experiments on the propagation of exciton packets in semiconductors. In these experiments, the excitonic transport under the action of a laser pulse has been studied. It turned out that under certain conditions this transport becomes anomalous and the excitons propagate through the crystal in a wave packet without diffusion. We propose a model for this phenomenon which relies on the presence of an exciton-phonon interaction and the formation of exciton-phonon condensate. In this model, the subsonic exciton propagation is described by soliton solutions of the nonlinear Schrödinger equation. The theory predicts two critical velocities for propagation of the packet, and this is in a good qualitative agreement with experimental data. In addition, we explain the results of experiments on strong nonlinear interactions between moving excitonic packets by introducing the exciton-phonon droplets with Bose-cores inside them. Such cores are characterized by a finite correlation length and can be considered as a kind of Bose-Einstein condensate.; We also study a model of a nonideal Bose-gas moving in a channel. It is known that the vortex model of superfluid dissipation cannot predict correctly the value of the critical velocity of superfluidity in planar geometry. We show that the existence of superfluidity in the Bose-gas can depend on the strength of the boundary interactions with channel walls. Indeed, if the dilute moving Bose-gas interacts with the walls via hard-core repulsion, boundary (boson-phonon) excitations can be introduced. They can reduce the value of the critical velocity of the superfluid. Such surface modes seem to exist in “soft matter” containers with flexible walls; they can be one of the sources of friction in anomalous excitonic transport in semiconductor heterostructures as well. |
