Difference equations in condensed matter physics and their application to exciton systems in thin molecular films

The main goal of this work is the development of the correct methodology of calculation of the Greenʹs function of broken symmetry structures. The two methods were analysed and it was concluded that the direct method with the use of the translational operators is not convenient for the analyses of the exciton properties in thin molecular films. The second proposed method, consisting in translation of the difference equation with spatially variable parameter into the system of difference equations with constant parameters, was applied to thin molecular film and the solution of this system, being Greenʹs function depending on two spatial indices, separately, was found exactly. With help of this Greenʹs function the spatial dependence of exciton concentration was found. The significance of the obtained spatial dependence of exciton concentration is discussed and it was concluded that on the basis of the found spatial dependence of exciton concentration can be determined such boundary conditions of thin molecular film which lead to high exciton concentrations and consequently to the possibility of construction of high power lasers.