Trudy Mat. Inst. Steklova, 2021, Volume 313, Pages 263–274
Derivation of the Redfield Quantum Master Equation and Corrections to It by the Bogoliubov Method
A. S. Trushechkin
Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we derive the Redfield quantum linear master equation, which is widely used in the theory of open quantum systems. This method allows one to calculate the joint state of a system and a reservoir at every instant of time, as well as to obtain quantum master equations as autonomous differential equations in an arbitrary order of perturbation theory. We prove that under certain conditions the expressions for the corrections of all orders are well defined. We also discuss the question of whether the quantum dynamics described by the derived quantum master equations is Markovian.
|Russian Science Foundation
|This work is supported by the Russian Science Foundation under grant 17-71-20154.
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Proceedings of the Steklov Institute of Mathematics, 2021, 313, 246–257
Received: September 6, 2020
Revised: November 28, 2020
Accepted: March 10, 2021
A. S. Trushechkin, “Derivation of the Redfield Quantum Master Equation and Corrections to It by the Bogoliubov Method”, Mathematics of Quantum Technologies, Collected papers, Trudy Mat. Inst. Steklova, 313, Steklov Math. Inst., Moscow, 2021, 263–274; Proc. Steklov Inst. Math., 313 (2021), 246–257
Citation in format AMSBIB
\paper Derivation of the Redfield Quantum Master Equation and Corrections to It by the Bogoliubov Method
\inbook Mathematics of Quantum Technologies
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\publ Steklov Math. Inst.
\jour Proc. Steklov Inst. Math.
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