Geodesic
Application of the Jacobi functional equation and the ATS theorem in a quantum optical model
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1860-1881

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A new method is devised to study the atomic inversion in the model of a two-level atom interacting with a single quantized mode of the (initially coherent) electromagnetic field in an ideal resonant cavity. The method is based on number-theoretic results applied to the approximation of special series, specifically, on the functional equation for Jacobi theta functions and the ATS theorem. New asymptotic formulas are derived, with the help of which the behavior of the atomic inversion function on various time intervals can be determined in detail depending on the parameters of the system. 
@article{ZVMMF_2017_57_11_a9,
     author = {E. A. Karatsuba},
     title = {Application of the {Jacobi} functional equation and the {ATS} theorem in a quantum optical model},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1860--1881},
     publisher = {mathdoc},
     volume = {57},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a9/}
}
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E. A. Karatsuba. Application of the Jacobi functional equation and the ATS theorem in a quantum optical model. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1860-1881. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a9/