Skip to main content
Log in

Wave-particle duality of solitons and solitonic analog of the Ramsauer-Townsend effect

  • Regular Article
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We show that the scaling symmetry breaking in soliton scattering reveals the hidden role of the soliton self-interaction (“binding”) energy and its dramatic impact on the wave-particle duality of solitons. Solitonic analog of the de Broglie wavelength and phenomenon similar to the Ramsauer-Taunsend effect can be discovered for Schrödinger solitons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L. de Broglie, The wave nature of the electron, Nobel Lecture (1929), pp. 244–256, Biography (World Scientific, 1998), pp. 257–259

  2. E. Schrödinger, The fundamental idea of wave mechanics, Nobel Lecture (1933), pp. 305–316, Biography (World Scientific, 1998), pp. 317–319

  3. W.C. Price, S.S. Chissick, T. Ravensdale, L. de Broglie, Wave Mechanics: the First Fifty Years (Wiley, New York, 1973)

  4. P.L. Christiansen, M.P. Sorensen, A.C. Scott, Nonlinear Science at the Dawn of the 21st Century (Springer, 2000)

  5. J.R. Taylor, Optical Solitons: Theory and Experiments (Cambridge University Press, 1992)

  6. Massive WDM and TDM Soliton Transmission Systems, edited by A. Hasegawa (Kluwer Academic Publishers, Dordrecht/Norwell, MA, 2000)

  7. G.P. Agrawal, Nonlinear Fiber Optics, 3rd edn. (Academic Press, San Diego, 2001)

  8. C. Rebbi, G. Soliani, Solitons and Particles (World Scientific, Singapore, 1984)

  9. N.S. Manton, Nonlinearity 21, T221 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. P.G. Drazin, R.S. Johnson, Solitons: an Introduction (Cambridge University Press, Cambridge, 1989)

  11. L.M. Kovachev, Physica D 190, 78 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. L.M. Kovachev, Int. J. Math. Math. Sci. 24, 1403 (2004)

    Article  MathSciNet  Google Scholar 

  13. Yu.P. Rybakov, B. Saha, Annales de la Fondation Louis de Broglie 26, 381 (2001)

    MathSciNet  Google Scholar 

  14. T.L. Belyaeva, V.N. Serkin, C. Hernandez-Tenorio, F. Garcia-Santibañez, J. Mod. Opt. 57, 1087 (2010)

    Article  ADS  MATH  Google Scholar 

  15. E. Schrödinger, Naturwissenschaften 14, 664 (1926), English translation in: The continuous transition from Micro- to Macro-Mechanics, Collected papers on wave mechanics (Chelsea Publishing Company, New York, 1978), pp. 41–44

    Article  ADS  Google Scholar 

  16. T.L. Belyaeva, V.N. Serkin, Internet Electronic J. Nanociencia et Moletrónica 9, 1715 (2011)

    Google Scholar 

  17. L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 64, 023601 (2001)

    Article  ADS  Google Scholar 

  18. K.T. Stoychev, M.T. Primatarowa, R.S. Kamburova, Phys. Rev. E 70, 066622 (2004)

    Article  ADS  Google Scholar 

  19. M. Peccianti, A. Daydyusha, M. Kaczmarek, G. Assanto, Nat. Phys. 2, 737 (2006)

    Article  Google Scholar 

  20. C. Lee, J. Brand, Europhys. Lett. 73, 321 (2006)

    Article  ADS  Google Scholar 

  21. Y. Linzon et al., Phys. Rev. Lett. 99, 133901 (2007)

    Article  ADS  Google Scholar 

  22. V. Ahufinger, A. Mebrahtu, R. Corbalán, A. Sanpera, New J. Phys. 9, 4 (2007)

    Article  ADS  Google Scholar 

  23. S. Masuda, K. Nakamura, Phys. Rev. A 78, 062108 (2008)

    Article  ADS  Google Scholar 

  24. R. Yang, X. Wu, Opt. Express 16, 17759 (2008)

    Article  ADS  Google Scholar 

  25. V.E. Demidov, U.H. Hansen, S.O. Demokritov, Phys. Rev. B 78, 054410 (2008)

    Article  ADS  Google Scholar 

  26. A. Barak, O. Peleg, C. Stucchio, A. Soffer, M. Segev, Phys. Rev. Lett. 100, 153901 (2008)

    Article  ADS  Google Scholar 

  27. T. Ernst, J. Brand, Phys. Rev. A 81, 033614 (2010)

    Article  ADS  Google Scholar 

  28. W. Wan, S. Muenzel, J.W. Fleischer, Phys. Rev. Lett. 104, 073903 (2010)

    Article  ADS  Google Scholar 

  29. C.P. Jisha, A. Alberucci, R.-K. Lee, G. Assanto, Opt. Lett. 36, 1848 (2011)

    Article  Google Scholar 

  30. R.W. Hasse, Phys. Rev. A 25, 583 (1982)

    Article  ADS  Google Scholar 

  31. M.A. de Moura, Phys. Rev. A 37, 4998 (1988)

    Article  ADS  Google Scholar 

  32. L.E. Ballentine, Y. Yang, J.P. Zibin, Phys. Rev. A 50, 2854 (1994)

    Article  ADS  Google Scholar 

  33. L.E. Ballentine, Quantum Mechanics: a Modern Development (World Scientific, 1998)

  34. T. Tsuzuki, J. Low Temp. Phys. 4, 441 (1971)

    Article  ADS  Google Scholar 

  35. L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)

    MathSciNet  Google Scholar 

  36. E.P. Gross, Nuovo Cimento 20, 454 (1961)

    Article  MATH  Google Scholar 

  37. E. Merzbacher, Quantum Mechanics, 3rd edn. (John Wiley & Sons, 1998)

  38. G. Pöschl, E. Teller, Z. Phys. 83, 143 (1933)

    Article  ADS  Google Scholar 

  39. N. Rosen, P.M. Morse. Phys. Rev. 42, 210 (1932)

    ADS  Google Scholar 

  40. R.J. Glauber, Phys. Rev. 131, 2766 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  41. E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. T.C. Hernandez, V.E. Villargan, V.N. Serkin, G.M. Aguero, T.L. Belyaeva, M.R. Pena, L.L. Morales, Quantum Electron. 35, 778 (2005)

    Article  ADS  Google Scholar 

  43. C.H. Tenorio, E.V. Vargas, V.N. Serkin, M.A. Granados, T.L. Belyaeva, R.P. Moreno, L.M. Lara, Quantum Electron. 35, 929 (2005)

    Article  ADS  Google Scholar 

  44. V.N. Serkin, T.L. Belyaeva, G.H. Corro, M.A. Granados, Quantum Electron. 33, 325 (2003)

    Article  ADS  Google Scholar 

  45. V.N. Serkin, T.L. Belyaeva, G.H. Corro, M.A. Granados, Quantum Electron. 33, 456 (2003)

    Article  ADS  Google Scholar 

  46. C. Ramsauer, Ann. Phys. 4, 513 (1921)

    Article  Google Scholar 

  47. V.A. Bailey, J.S. Townsend, Phil. Mag. 6, 873 (1921)

    Google Scholar 

  48. L.M. Kovachev, Opt. Express 15, 10318 (2007)

    Article  ADS  Google Scholar 

  49. L.M. Kovachev, J. Mod. Opt. 55, 2975 (2008)

    Article  Google Scholar 

  50. J. Leuthold, C. Foos, W. Freude, Nature Photonics 4, 535 (2010)

    Article  ADS  Google Scholar 

  51. D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)

    Article  ADS  Google Scholar 

  52. E. Witkowska, P. Deuar, M. Gajda, K. Rzkazewski, Phys. Rev. Lett. 106, 135301 (2011)

    Article  ADS  Google Scholar 

  53. F. Cattani, A. Kim, D. Anderson, M. Lisak, Phys. Rev. A 83, 013608 (2011)

    Article  ADS  Google Scholar 

  54. K. Nakamura, Z.A. Sobirov, D.U. Matrasulov, S. Sawada, Phys. Rev. E 84, 026609 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. N. Serkin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belyaeva, T.L., Serkin, V.N. Wave-particle duality of solitons and solitonic analog of the Ramsauer-Townsend effect. Eur. Phys. J. D 66, 153 (2012). https://doi.org/10.1140/epjd/e2012-30214-2

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2012-30214-2

Keywords

Navigation