Geodesic
Kinetic State and Emergence of Markovian Dynamics in Exactly Solvable Models of Open Quantum Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 198-224

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Typically, the theory of open quantum systems studies the dynamics of the reduced state (density operator) of the system. However, in the early stages of evolution, it is impossible to separate the reservoir dynamics from the system dynamics. Among the consequences of this fact is the violation of the positivity of solutions of some quantum master equations for the reduced density operator. In this paper we study the joint dynamics of the system and reservoir at an early stage of evolution and the pre-relaxation of the joint state to a so-called kinetic state. A kinetic state of the system and reservoir is characterized by the fact that it is completely determined by the reduced density operator of the system alone. Only after the formation of a kinetic state, it becomes possible to describe the evolution of the reduced density operator of the system in terms of a semigroup.
Keywords: open quantum systems, quantum master equations, Bogolyubov–van Hove limit, pre-relaxation. 
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     author = {A. S. Trushechkin},
     title = {Kinetic {State} and {Emergence} of {Markovian} {Dynamics} in {Exactly} {Solvable} {Models} of {Open} {Quantum} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {198--224},
     publisher = {mathdoc},
     volume = {324},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2024_324_a17/}
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A. S. Trushechkin. Kinetic State and Emergence of Markovian Dynamics in Exactly Solvable Models of Open Quantum Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Noncommutative Analysis and Quantum Information Theory, Tome 324 (2024), pp. 198-224. http://geodesic.mathdoc.fr/item/TM_2024_324_a17/