The appearance and properties of the structures in the density distribution of indirect excitons in a quantum well plane in semiconductors in an electric field have been studied for the case where a metallic electrode has a circular orifice. It has been shown that the inhomogeneous structures in the exciton density (islands and rings with an increased exciton density) appear, because the condensed exciton phase is present and the system is nonequilibrium due both to the finiteness of the exciton lifetime and to pumping. The dependences of the structure on the system parameters (window sizes, temperature, and pumping intensity) are in agreement with the experimental results reported by A.V. Gorbunov and V.B. Timofeev, Pis'ma Zh. Eksp. Teor. Fiz. 83, 178 (2006) [JETP Lett. 83, 146 (2006)]; Usp. Fiz. Nauk 176, 652 (2006) [Phys. Usp. 49, 629 (2006)]; Pis'ma Zh. Eksp. Teor. Fiz. 84, 390 (2006) [JETP Lett. 84, 329 (2006)].
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