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Mathematical Problems in Engineering
Volume 2012, Article ID 347674, 12 pages
Review Article

Mathematical Models of Dissipative Systems in Quantum Engineering

Academic Center of Optical Engineering and Photonics, Polytechnic University of Bucharest, 313 Spl. Independentei, 060042 Bucharest, Romania

Received 9 February 2012; Accepted 18 March 2012

Academic Editor: Ezzat G. Bakhoum

Copyright © 2012 Andreea Sterian and Paul Sterian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper shows the results of theoretical research concerning the modeling and characterization of the dissipative structures generally, the dissipation being an essential property of the system with self-organization which include the laser-type systems also. The most important results presented are new formulae which relate the coupling parameters 𝑎 𝑖 𝑛 from Lindblad equation with environment operators Γ 𝑖 ; microscopic quantitative expressions for the dissipative coefficients of the master equations; explicit expressions which describe the changes of the environment density operator during the system evolution for fermion systems coupled with free electromagnetic field; the generalized Bloch-Feynman equations for 𝑁 -level systems with microscopic coefficients in agreement with generally accepted physical interpretations. Based on Maxwell-Bloch equations with consideration of the interactions between nearing atomic dipoles, for the dense optical media we have shown that in the presence of the short optical pulses, the population inversion oscillates between two extreme values, depending on the strength of the interaction and the optical pulse energy.