Advertisement

Russian Physics Journal

, Volume 58, Issue 5, pp 606–615 | Cite as

Quasiparticles Described by the Gross–Pitaevskii Equation in the Semiclassical Approximation

  • A. E. Kulagin
  • A. Yu. Trifonov
  • A. V. Shapovalov
Article
  • 28 Downloads

Semiclassical asymptotics of the two-dimensional nonlocal Gross–Pitaevskii equation are constructed. The dynamics of the initial state, being a superposition of two wave packets, is investigated. The discrepancy of the obtained solution is investigated. The constructed asymptotic solutions are interpreted as a description of the interaction of two quasiparticles in the semiclassical approximation. A system of equations for the quasiparticle dynamics is obtained.

Keywords

nonlocal Gross–Pitaevskii equation semiclassical asymptotics quasiparticles 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. P. Pitaevskii, Usp. Fiz. Nauk, 168, 641–653 (1998).CrossRefGoogle Scholar
  2. 2.
    I. V. Simenog, Teor. Mat. Fiz., 30, No. 3, 208–214 (1977).MathSciNetCrossRefGoogle Scholar
  3. 3.
    V. P. Maslov, Sovr. Probl. Mat., VINITI, Moscow, 11, 153–234 (1978).Google Scholar
  4. 4.
    M. V. Karasev and V. P. Maslov, Sovr. Probl. Mat., VINITI, Moscow, 13, 145–267 (1979).Google Scholar
  5. 5.
    S. A. Vakulenko, V. P. Maslov, I. A. Molotkov, and A. I. Shafarevich, Dokl. Ross. Akad. Nauk, 345, 743–745 (1996).MathSciNetGoogle Scholar
  6. 6.
    V. V. Belov, A. Yu. Trifonov, and A. V. Shapovalov, Int. J. Math. Math. Sci. (USA), 32, No. 6, 325–370 (2002).MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    I. Bryuning, S. Yu. Dobrokhotov, R. V. Nekrasov, and A. I. Shafarevich, Teor. Mat. Fiz., 155, No. 2, 215–235 (2008).MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. V. Karasev, Mat. Zametki, 26, No. 6, 885–907 (1979).MathSciNetGoogle Scholar
  9. 9.
    M. V. Karasev and V. P. Maslov, Teor. Mat. Fiz. 40, No. 2, 235–244 (1979).MathSciNetCrossRefGoogle Scholar
  10. 10.
    V. V. Belov, E. K. Smirnova, and M. F. Kondrat’eva, Dokl. Ross. Akad. Nauk, 416, No. 2, 177–181 (2007).MATHMathSciNetGoogle Scholar
  11. 11.
    V. V. Belov and E. K. Smirnova, Mat. Zametki, 80, No. 2, 309–312 (2006).MathSciNetCrossRefGoogle Scholar
  12. 12.
    V. V. Belov, A. Yu. Trifonov, and A. V. Shapovalov, Teor. Mat. Fiz., 130, No. 3, 460–492 (2002).MathSciNetCrossRefGoogle Scholar
  13. 13.
    M. V. Karasev and V. P. Maslov, Nonlinear Poisson Brackets. Geometry and Quantization [in Russian], Nauka, Moscow (1991).Google Scholar
  14. 14.
    V. G. Bagrov, V. V. Belov, and A. Yu. Trifonov, Ann. Phys. (N.Y.), 246, No. 2, 231–280 (1996).MATHMathSciNetCrossRefADSGoogle Scholar
  15. 15.
    M. A. Malkin and V. I. Man’ko, Dynamical Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. E. Kulagin
    • 1
  • A. Yu. Trifonov
    • 1
    • 2
  • A. V. Shapovalov
    • 1
    • 2
  1. 1.National Research Tomsk Polytechnic UniversityTomskRussia
  2. 2.National Research Tomsk State UniversityTomskRussia

Personalised recommendations