Large fluctuations in two-level systems with stimulated emission
Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 133-144
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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.
@article{TMF_2019_198_1_a7,
author = {E. A. Pechersky and S. A. Pirogov and G. M. Sch\"utz and A. A. Vladimirov and A. A. Yambartsev},
title = {Large fluctuations in two-level systems with stimulated emission},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {133--144},
publisher = {mathdoc},
volume = {198},
number = {1},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a7/}
}
TY - JOUR AU - E. A. Pechersky AU - S. A. Pirogov AU - G. M. Schütz AU - A. A. Vladimirov AU - A. A. Yambartsev TI - Large fluctuations in two-level systems with stimulated emission JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2019 SP - 133 EP - 144 VL - 198 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a7/ LA - ru ID - TMF_2019_198_1_a7 ER -
%0 Journal Article %A E. A. Pechersky %A S. A. Pirogov %A G. M. Schütz %A A. A. Vladimirov %A A. A. Yambartsev %T Large fluctuations in two-level systems with stimulated emission %J Teoretičeskaâ i matematičeskaâ fizika %D 2019 %P 133-144 %V 198 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a7/ %G ru %F TMF_2019_198_1_a7
E. A. Pechersky; S. A. Pirogov; G. M. Schütz; A. A. Vladimirov; A. A. Yambartsev. Large fluctuations in two-level systems with stimulated emission. Teoretičeskaâ i matematičeskaâ fizika, Tome 198 (2019) no. 1, pp. 133-144. http://geodesic.mathdoc.fr/item/TMF_2019_198_1_a7/