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TMF, 2019, Volume 198, Number 1, Pages 133–144 (Mi tmf9545)  

Large fluctuations in two-level systems with stimulated emission

E. A. Pecherskya, S. A. Pirogova, G. M. Schützb, A. A. Vladimirova, A. A. Yambartsevc

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Interdisziplinäres Zentrum für Komplexe Systeme, Universität Bonn, Bonn, Germany
c Institute of Mathematics and Statistics, University of São Paulo, (USP), São Paulo, SP, Brazil

Abstract: We consider a system of $N$ identical independent Markov processes, each taking values $0$ or $1$. The system describes the stochastic dynamics of an ensemble of two-level atoms. The atoms are exposed to a photon flux. Under the photon flux action, each atom changes its state with some rates either from its ground state (state $0)$ to the excited state (state $1)$ or from the excited state to the ground state (stimulated emission). The atom can also spontaneously change its state from the excited to the ground state. We study rare events where a large cumulative emission occurs during a fixed time interval $[0,T]$. For this, we apply the large-deviation theory, which allows an asymptotic analysis as $N\to\infty$.

Keywords: continuous-time Markov process, large deviation, infinitesimal generator, Hamiltonian, Hamiltonian system.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
National Council for Scientific and Technological Development (CNPq) 301050/2016-3
Fundação de Amparo à Pesquisa do Estado de São Paulo 2017/10555-0
The research of E. A. Pechersky, S. A. Pirogov, and A. A. Vladimirov was performed at the Institute for Information Transmission Problems (IITP), Russian Academy of Sciences, and was supported by a grant from the Russian Science Foundation (Project No. 14-50-00150). The main contribution by S. A. Pirogov is in Sec. 5, the main contribution by A. A. Vladimirov is in Sec. 6, and the main contribution by E. A. Pechersky is in Sec. 7. The research of A. A. Yambartsev was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnolôgico (CNPq Grant No. 301050/2016-3) and the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP Grant No. 2017/10555-0).


DOI: https://doi.org/10.4213/tmf9545

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English version:
Theoretical and Mathematical Physics, 2019, 198:1, 118–128

Document Type: Article
Received: 14.02.2018
Revised: 14.02.2018

Citation: E. A. Pechersky, S. A. Pirogov, G. M. Schütz, A. A. Vladimirov, A. A. Yambartsev, “Large fluctuations in two-level systems with stimulated emission”, TMF, 198:1 (2019), 133–144; Theoret. and Math. Phys., 198:1 (2019), 118–128

Citation in format AMSBIB
\Bibitem{PecPirSch19}
\by E.~A.~Pechersky, S.~A.~Pirogov, G.~M.~Sch\"utz, A.~A.~Vladimirov, A.~A.~Yambartsev
\paper Large fluctuations in two-level systems with stimulated emission
\jour TMF
\yr 2019
\vol 198
\issue 1
\pages 133--144
\mathnet{http://mi.mathnet.ru/tmf9545}
\crossref{https://doi.org/10.4213/tmf9545}
\elib{http://elibrary.ru/item.asp?id=36603942}
\transl
\jour Theoret. and Math. Phys.
\yr 2019
\vol 198
\issue 1
\pages 118--128


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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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