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
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 $N\to\infty$.
continuous-time Markov process, large deviation, infinitesimal generator, Hamiltonian, Hamiltonian system.
|Russian Science Foundation
|National Council for Scientific and Technological Development (CNPq)
|Fundação de Amparo à Pesquisa do Estado de São Paulo
|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).
PDF file (412 kB)
First page: PDF file
Theoretical and Mathematical Physics, 2019, 198:1, 118–128
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
\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 Theoret. and Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|