Physica A: Statistical Mechanics and its Applications
Volume 353
,
1 August 2005,
Pages 217-234
doi:10.1016/j.physa.2005.01.022 
Copyright © 2005 Elsevier B.V. All rights reserved.
Difference equations in condensed matter physics and their application to exciton systems in thin molecular films
Vjekoslav Sajferta, 
, 
, Jovan Šetrajčićb, Dušan Popovc and Bratislav Tošićd
aTechnical Faculty “Mihajlo Pupin”,
Zrenjanin, University of Novi Sad, Djure Djakovica Street bb, Zrenjanin
23000, Serbia and Montenegro
bInstitute of Physics, Faculty of Sciences, Novi Sad, University of Novi Sad, Serbia and Montenegro
cUniversitatea “Politechnica”, Timisoara, Romania
dVojvodina Academy of Sciences and Arts, Novi Sad, University of Novi Sad, Serbia and Montenegro
Received 15 October 2004. Available online 16 February 2005.
Abstract
The main goal of this work is the development of
the correct methodology of calculation of the Green's 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 Green's function depending on two spatial indices,
separately, was found exactly. With help of this Green's 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.
Keywords: Difference equations; Variable coefficients; Operator solving; Excitons; Boundary conditions
PACS: 02.30.Vv; 02.60.Jh; 71.35.-y; 78.55.Kz; 78.66.-w
Corresponding author. Tel.:/fax: +38122554143.
