PESTRYAKOV A joint effect of exciton-phonon and exciton-exciton interactions on optical properties of semiconductors is studied. In these substances the exciton density is shown to be a mukivalued function of incident light intensity and the frequency and temperature conditions under which the optical bistability arises are specified. Investigation of nonlinear optical properties of semicondudora with account for the indirect phototransitions exhibits that both multistable optical states and the bistable ones distinguished by a complicated dynamics of the switching may be observed in such systems.

A canonical transformation which eliminates the trilinear exciton-phonon interaction and introduces new elementary excitations -"dressed" excitons -is proposed; it holds true both for the narrow and for broad exciton bands. The energy spectrum of the dressed excitons is investigated in detail for a one-dimensional model of Frenkel excitons interacting with optical phonons.Es wird eine kanonische Transformation vorgeschlagen, die die trilineare ExzitonPhonon-wechselwirkung eliminiert und neue Elementaranregungen,, ,bekleidete" Exzitonen, einfuhrt. Dies gilt sowohl fur schmale als auch f k breite Exzitonenbanden. Das Energiespektrum der bekleideten Exzitonen wird ausfuhrlich fur ein eindimensionales Model1 von Frenkel-Exzitonen, die mit optischen Phononen wechselwirken, untersucht.

The traditional theoretical treatment of the effects of the phonon subsystem on electron excitations in crystals is usually confined t o a consideration of the energy and phase relaxation of excitons. However, phonon effects do not amount only to the relaxation processes since they a r e also known to lead to self -trapping, formation of bound states, temperature shifts of exciton levels, and other physical phenomena specified by a change-over of the energy spectrum of the whole system. We draw attention to another important aspect of exciton-phonon interactions -"phonon clothing" of excitons /l/. Mathematically, the clothing may be described in terms of renormalization with the real part of the self-energy operator taken into account. As a result, the functional dependence of the exciton energy on quasi-momentum changes and split-off single-particle states may emerge. In crystals with great magnitudes of the oscillator strength of exciton

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