National Gallery of Art. John Walker

An approach to the many-exciton system

“…To take full account of the non-boson nature, we formally follow the procedure performed in the paper by Steyn-Ross and Gardiner (1983) 6) and ( 7) are not closed because they involve simultaneously both exciton and electron (hole) operators. Following Kaplan (1976) and owing to the reverse-t0-(3) relations (13)…”

“…In spite of their success in spectral problems many-exciton systems do not seem to be so well understood, especially from the statistical point of view. Kaplan (1976) formulated specific statistics of Frenkel excitons which then have been fruitfully utilised for researching the Bose-Einstein condensation (Kaplan and Ruvinskii 1976), the excitation-induced change of giant polariton dispersions (Avdjugin et af 1983;Nguyen 1988bNguyen , 1989a and the density and optical bi-stability (Nguyen 1988a) of excitons in molecular media.…”

“…In this paper we would like to extend Kaplan's results to Wannier-Mott excitons. Now, instead of exponent functions in unitary transformations connecting exciton operators in coordinate and momentum spaces (Kaplan 1976), we have to handle hydrogenlike functions describing the relative electron-hole motion in an exciton. This makes the situation quite confused and one hardly expects to obtain final results in a compact form!…”

Anomalies of polariton dispersion in photoexcited molecular crystals

“…Agranovich 1968, Hanamura 1974. For us, that explored by Kaplan (1976) and Kaplan and Ruvinskii (1976) seems to be best suited to the treatment of manyexciton systems with arbitrary exciton density, because they have been successful in finding a closed and exact set of commutation relations for Frenkel exciton operators, although some of them are trilinear but not bilinear as usual, namely Now we are going to study the intensity-dependence of the dispersion relations of the eigenmodes of the coupled photon-exciton system subjected to excitement by the external light field (1). To do this we shall follow two stages:…”

“…is the total exciton number. The specific form of the total exciton number operator f i x as seen from ( 17) is due to the non-bosonic nature of excitons (see Kaplan 1976). Now going to the energy representation by means of the transformation…”