A phenomenological theory of exciton condensation in conditions of inhomogeneous excitation is proposed. The theory is applied to the study of the development of an exciton luminescence ring and the ring fragmentation at macroscopical distances from the central excitation spot in coupled quantum wells. The transition between the fragmented and the continuous ring is considered. With assumption of a defect in the structure, a possibility of a localized island of the condensed phase in a fixed position is shown. Exciton density distribution is also analyzed in the case of two spatially separated spots of the laser excitation.

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Phase transitions in a system of indirect excitons in semiconductor double quantum wells are studied for a set-up when one of the electrodes is of finite size and, in particular, has the shape of a disc. At voltage a region under the rim of the disc is created where excitons have lower energy, thus providing a macroscopic trap attractive for excitons while being repulsive for charged particles. The theory of the formation of patterns of the excitonic condensed phase under the disc is built based on the assumption of the existence of the inter-exciton range where the interaction between them is attractive. The finite value of the exciton lifetime is taken into account serving as a limiting factor for the size of the islands of the condensed phase. The calculations reveal complex restructuring of the patterns of the spatial distribution of exciton density with increasing pumping intensity: from the structureless gaseous phase to separate islands of the condensed phase within the gaseous phase, then to islands of the gaseous phase in the bulk of the condensed phase and finally to the continuous condensed phase.

The appearance of the non-homogeneous structures of the indirect exciton density distribution in the region of the quantum well (in the region of the inner ring) is explained. The structure (the fragmentation) occurs due to the exciton condensed phase formation because of interaction between excitons. The formation of the structure is related with the non-equalibrity of the system, which is caused by the exciton finite lifetime and the presence of the pumpimg. The structure emerges in the shape of a set of islands or circles of the condensed phase. The structure type depends on the pumping intensity, the size of the laser spot and disappears with increasing the temperature. The merging of two structures, created by different laser spots, is investigated at decreasing the distance between the centers of the spots.

We study the development of ring luminescence of indirect excitons at macroscopical distances from the central excitation spot in quantum well structures. The Landau model for exciton condensation generalized for particles with finite lifetimes in conditions of inhomogeneous excitation is proposed. The transition between the fragmented and continuous rings and the temperature dependence of the effects are considered. The irradiation of the system by two spatially separated laser spots is simulated as well.

The condensation of indirect excitons in double quantum wells is studied in an electric field created by electrodes of different shapes. The finite value of the exciton lifetime, the pumping and nonuniformity of the electric field under the electrode are taken into account. It is shown that islands of exciton condensed phase emerge under electrodes when the pumping exceeds a certain threshold value. They appear first under the rim where the potential energy of excitons has a dip. Calculations predict a complicated evolution of the exciton density distribution: from the gaseous phase at low laser intensities to the condensed phase in the whole area under the electrode at larger intensities. Therefore, the configurations of the exciton condensed phase may be manipulated by choosing the setups with conductive electrodes of different shapes via forming specific potentials of the electrical field and controlled by the level of the laser irradiation.

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