Davydov free excitons

The operator ((, t) is the free exciton field. As a first step we are going to show that the c-number Davydov soliton ... 

In the following 20 years, a group of physicists in the Ukraine [2] studied a series of other aromatic crystals spectroscopically. It developed that there are also very characteristic differences from the spectra of free molecules. In the year 1948, A. S. Davydov [3] formulated the basic theoretical explanation for the observable interaction processes in the crystal spectra, between the molecules in electronically excited states within the crystal. He made use of the model of Frenkel excitons [4] and was able in particular to give a quantitative explanation of a characteristic line splitting, the Davydov splitting, as a fundamental property of organic molecular crystals. Fig. 6.1 shows as an example the splitting of the 0,0-transition in the Ti So absorption spectrum of anthracene at room temperature. 

The spectrum depends on the solvent. The solvent may be a crystal, in which case there is a small red-shift (to longer wavelengths) of the absorption compared to the free molecule. Furthermore, there is a formation of excitons. Local excitons are referred to as Frenkel excitons. Excitons extended over the whole crystal have been studied in great detail by Davydov and are called Davydov excitons. The lowest exciton state is further red-shifted compared to the free molecule absorption. Local excitons polarize themselves and the medium (Figure 18.3). As usual, when the reorganization energy is less than the coupling, the excitons are delocalized. 

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