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On the Decay of an “Isolated” Oscillator Nonlinearly Coupled to a Damped Oscillator

  • Nonlinear Phenomena
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Abstract

Mechanisms of pumping and decay of an “isolated” oscillator which can nonlinearly interact with a neighboring oscillator having a different frequency have been discussed. It has been shown that, if this neighboring oscillator is coupled to a broadband thermostat field, the isolated oscillator begins to interact with this thermostat field. As a result, a new relaxation channel appears because of the quantum interference of interacting systems, which can hardly be explained within traditional approaches.

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References

  1. C. W. Gardiner and R Zoller, Quantum Noise (Springer, Berlin, 2004).

    MATH  Google Scholar 

  2. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge Univ. Press, Cambridge, 2009).

    Book  Google Scholar 

  3. A. S. Kholevo, Quantum Systems, Channels, Information (MTsNMO, Moscow, 2010) [in Russian].

    Google Scholar 

  4. M. Lax, Phys. Rev. 145, 110 (1966).

    Article  ADS  Google Scholar 

  5. M. Lax, Opt. Commun. 179, 463 (2000).

    Article  ADS  Google Scholar 

  6. P. D. Drummond, K. J. McNeil, and D. F Walls, Opt. Acta 28, 211 (1981).

    Article  ADS  Google Scholar 

  7. Yu. E. Lozovik, V. G. Tsvetus, and E. A. Vinogradov, JETPLett. 61, 723 (1995).

    ADS  Google Scholar 

  8. S.V. Remizov, D. S. Shapiro, and A. N. Rubtsov, JETP Lett. 105, 130 (2017).

    Article  ADS  Google Scholar 

  9. E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T.J. Kippenberg, Nature (London, U.K.) 482, 63 (2012).

    Article  ADS  Google Scholar 

  10. C. Joshi, P. Ohberg, J. D. Cresser, and E. Andersson, Phys. Rev. A 90, 063815 (2014).

    Article  Google Scholar 

  11. D. F Walls, Z. Phys. 234, 231 (1970).

    Article  ADS  Google Scholar 

  12. A. E. Teretenkov, Mat. Zam. 100, 636 (2016).

    Article  MathSciNet  Google Scholar 

  13. A. I. Trubilko and A. M. Basharov, J. Exp. Theor. Phys. 129, 339 (2019).

    Article  ADS  Google Scholar 

  14. D. N. Klyshko, Photons Nonlinear Optics (Nauka, Moscow, 1980; CRC, Boca Raton, 1988).

    Google Scholar 

  15. Y. R. Shen, The Principle of Nonlinear Optics (Wiley-Interscience, New York, 1984).

    Google Scholar 

  16. A. M. Basharov, J. Exp. Theor. Phys. 126, 310 (2018).

    Article  ADS  Google Scholar 

  17. N. M. Krylov and N. N. Bogolyubov, Introduction to Non-linear Mechanics (RKhD, Moscow, 2004; Princeton Univ. Press, Princeton, 1950).

    Google Scholar 

  18. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations (GIFML, Moscow, 1958; Gordon and Breach, New York, 1962).

    MATH  Google Scholar 

  19. V S. Butylkin, A. E. Kaplan, Yu. G. Khronopulo, and E. I. Yakubovich, Resonant Nonlinear Interactions of light with Matter (Nauka, Moscow, 1977; Springer, Berlin, Heidelberg, 1989).

    Google Scholar 

  20. A. I. Maimistov and A. M. Basharov, Nonlinear Optical Waves (Kluwer Academic, Dordrecht, 1999).

    Book  Google Scholar 

  21. V N. Bogaevski and A. Povzner, Algebraic Methods in Nonlinear Perturbation Theory (Springer, New York, 1991).

    Book  Google Scholar 

  22. A. M. Basharov, J. Exp. Theor. Phys. 115, 376 (2012).

    Article  ADS  Google Scholar 

  23. G. Lindblad, Commun. Math. Phys. 40, 147 (1975).

    Article  ADS  Google Scholar 

  24. V Gorini, A. Kossakowski, and E. C. G. Sundarsham, J. Math. Phys. 17, 821 (1976).

    Article  ADS  Google Scholar 

  25. A. M. Basharov, Phys. Lett. A 376, 1881 (2012).

    Article  ADS  Google Scholar 

  26. L. V Keldysh, V. D. Kulakovskii, S. Reitzenstein, M. N. Makhonin, and A. Forchel, JETP Lett. 84, 494 (2006).

    Article  ADS  Google Scholar 

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Acknowledgments

We are grateful to Prof. A.I. Maimistov for stimulating discussions of nonlinear interactions.

Funding

This work was supported in part by the Russian Foundation for Basic Research (project no. 19-02-00234a).

Author information

Authors and Affiliations

  1. St. Petersburg University of State Fire Service of Emercom of Russia, St. Petersburg, 196105, Russia

    A. I. Trubilko

  2. National Research Center Kurchatov Institute, Moscow, 123182, Russia

    A. M. Basharov

  3. Department of Mathematics and Mathematical Methods of Physics, Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow region, 141701, Russia

    A. M. Basharov

Authors
  1. A. I. Trubilko
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  2. A. M. Basharov
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Corresponding author

Correspondence to A. I. Trubilko.

Additional information

Russian Text © The Author(s), 2019, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2019, Vol. 110, No. 7, pp. 505—511.

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Trubilko, A.I., Basharov, A.M. On the Decay of an “Isolated” Oscillator Nonlinearly Coupled to a Damped Oscillator. Jetp Lett. 110, 517–522 (2019). https://doi.org/10.1134/S0021364019190123

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  • DOI: https://doi.org/10.1134/S0021364019190123

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