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Tr. Mat. Inst. Steklova, 2019, Volume 306, Pages 273–286 (Mi tm4020)  

Dynamics of Reservoir Observables within the Zwanzig Projection Operator Method in the Theory of Open Quantum Systems

A. S. Trushechkinab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b National University of Science and Technology MISIS, Leninskii pr. 4, Moscow, 119049 Russia

Abstract: One of the main methods for describing the dynamics of open quantum systems is the method of quantum master equations. These equations describe the dynamics of the reduced density operator of a system interacting with a reservoir. In this case, averaging is performed over the degrees of freedom of the reservoir, which does not allow one to describe the dynamics of reservoir observables. In this paper we show that applying the Zwanzig projection operator method, which is used in deriving quantum master equations, one can also derive dynamic equations for reservoir observables. As an example, we derive dynamic equations for the average number of quanta (photons, phonons) of a bosonic reservoir in the approximation of its weak coupling to the system in the case of the dipole interaction Hamiltonian.

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/tm4020

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English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 306, 257–270

Bibliographic databases:

UDC: 517.958:530.145
Received: October 2, 2018
Revised: October 5, 2018
Accepted: May 14, 2019

Citation: A. S. Trushechkin, “Dynamics of Reservoir Observables within the Zwanzig Projection Operator Method in the Theory of Open Quantum Systems”, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019, 273–286; Proc. Steklov Inst. Math., 306 (2019), 257–270

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\paper Dynamics of Reservoir Observables within the Zwanzig Projection Operator Method in the Theory of Open Quantum Systems
\inbook Mathematical physics and applications
\bookinfo Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov
\serial Tr. Mat. Inst. Steklova
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\vol 306
\pages 273--286
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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