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The gas of interacting excitons in quantum wells is studied. We obtain theHamiltonian of this gas by the projection of the electron-hole plasmaHamiltonian to exciton states and an expansion in a small density. Matrixelements of the exciton Hamiltonian are rather sensitive to the geometry of theheterostructure. The mean field approximation of the exciton Hamiltonian givesthe blue shift and spin splitting of the exciton luminescence lines. We alsowrite down the Boltzmann equation for excitons and estimate the energy and spinrelaxation time resulting from the exciton-exciton scattering. Making use ofthese calculations we succeeded to explain some recent experimental resultswhich have not been explained so far.Comment: 51 pages, 4 figur

Exciton-exciton interactions in quantum wells: Optical properties and energy and spin relaxation