Excitonic Bloch equations for a two-dimensional system of interacting excitons

We derive the effective Bose Hamiltonian for a system of interacting excito ns applying the Usui transformation. The fermionic nonlinearities are consi stently included, leading to a density dependent correction to the kinetic Hamiltonian and to a saturation of the exciton oscillator strength. The exc iton-exciton interaction potentials due to the Coulomb interaction are calc ulated, accounting for the spin dependence. Starting from the effective Ham iltonian, we obtain the excitonic Bloch equations. As a first application, we study the problem of excitonic Rabi oscillations in quantum wells.