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TMF, 2018, Volume 194, Number 2, Pages 259–276 (Mi tmf9395)  

Algebraic aspects of the dynamics of quantum multilevel systems in the projection operator technique

N. N. Bogolyubov (Jr.), A. V. Soldatov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Using the projection operator method, we obtain approximate time-local and time-nonlocal master equations for the reduced statistical operator of a multilevel quantum system with a finite number $N$ of quantum eigenstates coupled simultaneously to arbitrary classical fields and a dissipative environment. We show that the structure of the obtained equations is significantly simplified if the free Hamiltonian dynamics of the multilevel system under the action of external fields and also its Markovian and non-Markovian evolutions due to coupling to the environment are described via the representation of the multilevel system in terms of the $SU(N)$ algebra, which allows realizing effective numerical algorithms for solving the obtained equations when studying real problems in various fields of theoretical and applied physics.

Keywords: multilevel quantum system, abbreviated description, projection operator, open system, unitary group generator, operation algebra, master equation, expansion in terms of a system of orthogonal polynomials.

DOI: https://doi.org/10.4213/tmf9395

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English version:
Theoretical and Mathematical Physics, 2018, 194:2, 220–235

Document Type: Article
PACS: 05.30.-d; 42.50.-p; 05.10.-a; 02.70.-c; 03.65.Aa; 03.65.Yz; 02.60.Cb; 02.30.Mv
MSC: 82C10; 81V80; 82D80
Received: 01.05.2017

Citation: N. N. Bogolyubov (Jr.), A. V. Soldatov, “Algebraic aspects of the dynamics of quantum multilevel systems in the projection operator technique”, TMF, 194:2 (2018), 259–276; Theoret. and Math. Phys., 194:2 (2018), 220–235

Citation in format AMSBIB
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\by N.~N.~Bogolyubov (Jr.), A.~V.~Soldatov
\paper Algebraic aspects of the~dynamics of quantum multilevel systems in
the~projection operator technique
\jour TMF
\yr 2018
\vol 194
\issue 2
\pages 259--276
\mathnet{http://mi.mathnet.ru/tmf9395}
\crossref{https://doi.org/10.4213/tmf9395}
\elib{http://elibrary.ru/item.asp?id=34940694}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 194
\issue 2
\pages 220--235


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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