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 Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 276–286 (Mi tm3917)

Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional

A. S. Trushechkinabc

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia
c National University of Science and Technology MISIS, Leninskii pr. 4, Moscow, 119049 Russia

Abstract: A necessary and sufficient condition is derived for a density operator to be a stationary solution for a certain class of Lindblad equations in the theory of open quantum systems. This condition is based on the properties of a functional that in some cases corresponds to entropy production. Examples are given where this condition is used to find stationary solutions.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-2815.2017.1 This work was supported by a grant of the President of the Russian Federation, project no. MK-2815.2017.1.

DOI: https://doi.org/10.1134/S0371968518020206

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 262–271

Bibliographic databases:

UDC: 517.958:530.145.6

Citation: A. S. Trushechkin, “Finding stationary solutions of the Lindblad equation by analyzing the entropy production functional”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 276–286; Proc. Steklov Inst. Math., 301 (2018), 262–271

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3917
• https://doi.org/10.1134/S0371968518020206
• http://mi.mathnet.ru/eng/tm/v301/p276

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This publication is cited in the following articles:
1. A. S. Trushechkin, “Dynamics of Reservoir Observables within the Zwanzig Projection Operator Method in the Theory of Open Quantum Systems”, Proc. Steklov Inst. Math., 306 (2019), 257–270
2. A. K. Guschin, “Obobscheniya prostranstva nepreryvnykh funktsii; teoremy vlozheniya”, Matem. sb., 211:11 (2020), 54–71
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