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An Example of Explicit Generators of Local and Nonlocal Quantum Master Equations

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Abstract

A simple example of completely positive dynamics is considered for which both the generator of a nonlocal integro-differential equation leading to such dynamics and the time-local generator can be calculated explicitly. It is demonstrated that introducing a small parameter in this simple example allows one to reproduce some nonperturbative phenomena that occur in more realistic models. In addition, a special case of fermionic dynamics is considered, and it is shown that one can actually find families of moments whose dynamics is linear but satisfies non-Markovian equations.

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Funding

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

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  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    A. E. Teretenkov

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  1. A. E. Teretenkov
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Correspondence to A. E. Teretenkov.

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Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 313, pp. 253–262 https://doi.org/10.4213/tm4160.

Translated by I. Nikitin

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Teretenkov, A.E. An Example of Explicit Generators of Local and Nonlocal Quantum Master Equations. Proc. Steklov Inst. Math. 313, 236–245 (2021). https://doi.org/10.1134/S0081543821020218

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  • DOI: https://doi.org/10.1134/S0081543821020218

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