Application of Perturbation Theory to a Master Equation

Application of Perturbation Theory to a Master Equation

We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order co...

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Main Authors: B. M. Villegas-Martínez, F. Soto-Eguibar, H. M. Moya-Cessa
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2016/9265039
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spelling doaj-d3e4428f50bd4ca6b8e548d63862baf42021-07-02T02:53:33ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/92650399265039Application of Perturbation Theory to a Master EquationB. M. Villegas-Martínez0F. Soto-Eguibar1H. M. Moya-Cessa2Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE, Calle Luis Enrique Erro 1, 72840 Santa María Tonantzintla, PUE, MexicoInstituto Nacional de Astrofísica, Óptica y Electrónica, INAOE, Calle Luis Enrique Erro 1, 72840 Santa María Tonantzintla, PUE, MexicoInstituto Nacional de Astrofísica, Óptica y Electrónica, INAOE, Calle Luis Enrique Erro 1, 72840 Santa María Tonantzintla, PUE, MexicoWe develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating the Q-function, the average number of photons, and the distance between density matrices.http://dx.doi.org/10.1155/2016/9265039
collection DOAJ
language English
format Article
sources DOAJ
author B. M. Villegas-Martínez
F. Soto-Eguibar
H. M. Moya-Cessa
spellingShingle B. M. Villegas-Martínez
F. Soto-Eguibar
H. M. Moya-Cessa
Application of Perturbation Theory to a Master Equation
Advances in Mathematical Physics
author_facet B. M. Villegas-Martínez
F. Soto-Eguibar
H. M. Moya-Cessa
author_sort B. M. Villegas-Martínez
title Application of Perturbation Theory to a Master Equation
title_short Application of Perturbation Theory to a Master Equation
title_full Application of Perturbation Theory to a Master Equation
title_fullStr Application of Perturbation Theory to a Master Equation
title_full_unstemmed Application of Perturbation Theory to a Master Equation
title_sort application of perturbation theory to a master equation
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2016-01-01
description We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the known exact analytic solution. The comparison is done by calculating the Q-function, the average number of photons, and the distance between density matrices.
url http://dx.doi.org/10.1155/2016/9265039
work_keys_str_mv AT bmvillegasmartinez applicationofperturbationtheorytoamasterequation
AT fsotoeguibar applicationofperturbationtheorytoamasterequation
AT hmmoyacessa applicationofperturbationtheorytoamasterequation
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