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Reduced Dynamics of the Wigner Function

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Abstract

In the paper, we derive a formula expressing the reduced dynamics of the Wigner function using the dynamics of the Wigner function of a larger system. Here the latter system is assumed to be isolated and generating the dynamics of its subsystem.

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References

  1. V. I. Bogachev and O. G. Smolyanov, Real and Functional Analysis (Moscow-Izhevsk, 2011; Springer, 2020).

  2. J. Gough, T. S. Ratiu, and O. G. Smolyanov, “Feynman, Wigner, and Hamiltonian Structures Describing the Dynamics of Open Quantum Systems,” Dokl. Akad. Nauk 454(4), 379–383 (2014)

    MathSciNet  MATH  Google Scholar 

  3. J. Gough, T. S. Ratiu, and O. G. Smolyanov, [Dokl. Math. 89(1), 68–71 (2014)].

    Article  MathSciNet  Google Scholar 

  4. V. V. Kozlov and O. G. Smolyanov, “Wigner Function and Diffusion in Collisionfree Media of Quantum Particles,” Teor. Veroyatnost. i Primenen. 51(1), 1–13 (2006)

    Article  Google Scholar 

  5. V. V. Kozlov and O. G. Smolyanov, [Theory Probab. Appl. 51(1), 168–181 (2007).

    Article  MathSciNet  Google Scholar 

  6. I. Kupsch and O. G. Smolyanov, “Exact Master Equations Describing Reduced Dynamics of the Wigner Function,” Fundam. Prikl. Mat. 12(5), 203–219 (2006)

    MATH  Google Scholar 

  7. I. Kupsch and O. G. Smolyanov, [J. Math. Sci. 150(6), 2598–2608 (2008)].

    Article  MathSciNet  Google Scholar 

  8. I. D. Remizov and M. F. Starodubtseva, “Quasi-Feynman Formulas Providing Solutions of Multidimensional Schrödinger Equations with Unbounded Potential,” Mat. Zametki 104(5), 790–795 (2018)

    Article  MathSciNet  Google Scholar 

  9. I. D. Remizov and M. F. Starodubtseva, [Math. Notes 104(5), 767–772 (2018)].

    Article  MathSciNet  Google Scholar 

  10. I. D. Remizov, “Solution of the Schrödinger Equation with the Use of the Translation Operator,” Mat. Zametki 100(3), 477–480 (2016)

    Article  MathSciNet  Google Scholar 

  11. I. D. Remizov, [Math. Notes 100(3), 499–503 (2016)].

    Article  MathSciNet  Google Scholar 

  12. M. A. Shubin, Pseudodifferential Operators and Spectral Theory (Nauka, Moscow, 1978; Springer-Verlag, Berlin, 2001).

    MATH  Google Scholar 

  13. J. E. Moyal, “Quantum Mechanics as a Statistical Theory,” Proc. Cambridge Philos. Soc. 45(1), 99–124 (1949).

    Article  ADS  MathSciNet  Google Scholar 

  14. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Springer, London, 1992).

    Book  Google Scholar 

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Acknowledgment

The present research is related to the Laboratory of Infinite-Dimensional Analysis and Mathematical Physics of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University. The author also thanks O. G. Smolyanov for setting the problem and interest in the work.

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Correspondence to M. O. Burkatskii.

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Burkatskii, M.O. Reduced Dynamics of the Wigner Function. Russ. J. Math. Phys. 27, 18–21 (2020). https://doi.org/10.1134/S1061920820010021

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  • DOI: https://doi.org/10.1134/S1061920820010021

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