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On the Hierarchical Behavior of Solutions of the Maryland Equation in the Semiclassical Approximation

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References

  1. S. Jitomirskaya and W. Liu, Comm. Pure Appl. Math. 70 (6), 1025 (2017).

    Article  MathSciNet  Google Scholar 

  2. P. B. Wiegmann and A. V. Zabrodin, Nuclear Phys. B 422 (3), 495 (1994).

    Article  MathSciNet  Google Scholar 

  3. Ya. G. Sinai, J. Statist. Phys. 46 (5-6), 861 (1987).

    Article  MathSciNet  Google Scholar 

  4. B. Helffer and J. Sjöstrand, Analyse semi-classique pour l’équation de Harper (avec application à l’équation de Schrödinger avec champ magnétique), in Mém. Soc. Math. France (N. S.) (Soc. Math. France, Paris, 1988), Vol. 34.

    MATH  Google Scholar 

  5. A. A. Fedotov, St. Petersburg Math. J. 25 (2), 303 (2014).

    Article  MathSciNet  Google Scholar 

  6. A. Fedotov and F. Klopp, in Mathematical Results in Quantum Mechanics (World Sci. Publ., Hackensack, NJ, 2008), pp. 66–78.

    Article  Google Scholar 

  7. S. Jitomirskaya and W. Lui, Ann. of Math. (2) 187 (3), 721 (2018).

    Article  MathSciNet  Google Scholar 

  8. A. Ya. Khinchin, Continued Fractions (Nauka, Moscow, 1978) [in Russian].

    MATH  Google Scholar 

  9. B. Simon, Ann. Physics 159 (1), 157 (1985).

    Article  MathSciNet  Google Scholar 

  10. V. P. Maslov and M. V. Fedoryuk, Semiclassical Approximation for Equations of Quantum Mechanics (Nauka, Moscow, 1976) [in Russian].

    MATH  Google Scholar 

  11. A. Fedotov and F. Sandomirskyi, Comm. Math. Phys. 334 (2), 1083 (2015).

    Article  MathSciNet  Google Scholar 

  12. V. S. Buslaev and A. A. Fedotov, St. Petersburg Math. J. 6 (3), 495 (1995).

    MathSciNet  Google Scholar 

  13. A. A. Fedotov and E. V. Shchetka, St. Petersburg Math. J. 29 (2), 363 (2018).

    Article  MathSciNet  Google Scholar 

  14. A. Fedotov and F. Klopp, SIAM J. Math. Anal. 51 (6), 4413 (2019).

    Article  MathSciNet  Google Scholar 

  15. A. Fedotov and F. Klopp, Appl. Anal. (2019).

    Google Scholar 

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Funding

This work was carried out in the framework of a Russian–French project supported by CNRS, France (a PRC project) and supported by the Russian Foundation for Basic Research under grant no. 17-51-150008.

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Correspondence to F. Klopp.

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Klopp, F., Fedotov, A.A. On the Hierarchical Behavior of Solutions of the Maryland Equation in the Semiclassical Approximation. Math Notes 108, 906–910 (2020). https://doi.org/10.1134/S0001434620110346

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  • DOI: https://doi.org/10.1134/S0001434620110346

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