Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy Mat. Inst. Steklova, 2021, Volume 313, Pages 263–274 (Mi tm4184)  

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

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 17-71-20154
This work is supported by the Russian Science Foundation under grant 17-71-20154.


DOI: https://doi.org/10.4213/tm4184

Full text: PDF file (206 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2021, 313, 246–257

Bibliographic databases:

UDC: 517.958:530.145
Received: September 6, 2020
Revised: November 28, 2020
Accepted: March 10, 2021

Citation: 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
\Bibitem{Tru21}
\by A.~S.~Trushechkin
\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
\yr 2021
\vol 313
\pages 263--274
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4184}
\crossref{https://doi.org/10.4213/tm4184}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 313
\pages 246--257
\crossref{https://doi.org/10.1134/S008154382102022X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000674956500022}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85110645923}


Linking options:
  • http://mi.mathnet.ru/eng/tm4184
  • https://doi.org/10.4213/tm4184
  • http://mi.mathnet.ru/eng/tm/v313/p263

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:65
    References:4
    First page:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021