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The problem of an electron-hole system interacting through a contactpotential and moving in a one-dimensional quantum ring threaded by anAharonov-Bohm flux is considered, both with respect to the system's energeticsas well as its optical properties. An exact analytical expression for theenergy spectrum is derived using a straightforward method based on boundaryconditions for wavefunctions and their derivatives along the ring. The opticalproperties of this exciton system, namely the linear dynamic polarizability andabsorption spectrum are investigated demonstrating certain unusual features. Itis shown, for example, that for special values of the magnetic flux there areenergies in the spectrum that correspond to the dark excitonic states.

Linear dynamic polarizability and absorption spectrum of an exciton in a quantum ring in a magnetic field