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On Time-Dependent Projectors and a Generalization of the Thermodynamical Approach in the Theory of Open Quantum Systems

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Abstract

We develop a consistent perturbative technique for obtaining a time-local linear master equation based on projection methods in the case where the projection operator depends on time. Then we introduce a generalization of the Kawasaki–Gunton projection operator, which allows us to use this technique to derive, generally speaking, nonlinear master equations in the case of arbitrary ansatzes consistent with some set of observables. Most of the results obtained are of a very general nature, but when discussing them, we put emphasis on the application of these results to the theory of open quantum systems.

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Acknowledgments

The authors are sincerely grateful to G. Gasbarri, A. Yu. Karasev, E. O. Kiktenko, A. M. Savchenko, R. Singh, and A. S. Trushechkin for discussing the problems considered in the paper. The authors are also grateful to an anonymous referee for valuable comments that helped to significantly improve the text of the paper.

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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia

    Kh. Sh. Meretukov

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

    A. E. Teretenkov

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  1. Kh. Sh. Meretukov
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Correspondence to Kh. Sh. Meretukov or A. E. Teretenkov.

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Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Vol. 324, pp. 144–161 https://doi.org/10.4213/tm4371.

Translated by K. Shubik

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Meretukov, K.S., Teretenkov, A.E. On Time-Dependent Projectors and a Generalization of the Thermodynamical Approach in the Theory of Open Quantum Systems. Proc. Steklov Inst. Math. 324, 135–152 (2024). https://doi.org/10.1134/S0081543824010140

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