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.
Similar content being viewed by others
References
L. de Broglie, The wave nature of the electron, Nobel Lecture (1929), pp. 244–256, Biography (World Scientific, 1998), pp. 257–259
E. Schrödinger, The fundamental idea of wave mechanics, Nobel Lecture (1933), pp. 305–316, Biography (World Scientific, 1998), pp. 317–319
W.C. Price, S.S. Chissick, T. Ravensdale, L. de Broglie, Wave Mechanics: the First Fifty Years (Wiley, New York, 1973)
P.L. Christiansen, M.P. Sorensen, A.C. Scott, Nonlinear Science at the Dawn of the 21st Century (Springer, 2000)
J.R. Taylor, Optical Solitons: Theory and Experiments (Cambridge University Press, 1992)
Massive WDM and TDM Soliton Transmission Systems, edited by A. Hasegawa (Kluwer Academic Publishers, Dordrecht/Norwell, MA, 2000)
G.P. Agrawal, Nonlinear Fiber Optics, 3rd edn. (Academic Press, San Diego, 2001)
C. Rebbi, G. Soliani, Solitons and Particles (World Scientific, Singapore, 1984)
N.S. Manton, Nonlinearity 21, T221 (2008)
P.G. Drazin, R.S. Johnson, Solitons: an Introduction (Cambridge University Press, Cambridge, 1989)
L.M. Kovachev, Physica D 190, 78 (2004)
L.M. Kovachev, Int. J. Math. Math. Sci. 24, 1403 (2004)
Yu.P. Rybakov, B. Saha, Annales de la Fondation Louis de Broglie 26, 381 (2001)
T.L. Belyaeva, V.N. Serkin, C. Hernandez-Tenorio, F. Garcia-Santibañez, J. Mod. Opt. 57, 1087 (2010)
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
T.L. Belyaeva, V.N. Serkin, Internet Electronic J. Nanociencia et Moletrónica 9, 1715 (2011)
L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 64, 023601 (2001)
K.T. Stoychev, M.T. Primatarowa, R.S. Kamburova, Phys. Rev. E 70, 066622 (2004)
M. Peccianti, A. Daydyusha, M. Kaczmarek, G. Assanto, Nat. Phys. 2, 737 (2006)
C. Lee, J. Brand, Europhys. Lett. 73, 321 (2006)
Y. Linzon et al., Phys. Rev. Lett. 99, 133901 (2007)
V. Ahufinger, A. Mebrahtu, R. Corbalán, A. Sanpera, New J. Phys. 9, 4 (2007)
S. Masuda, K. Nakamura, Phys. Rev. A 78, 062108 (2008)
R. Yang, X. Wu, Opt. Express 16, 17759 (2008)
V.E. Demidov, U.H. Hansen, S.O. Demokritov, Phys. Rev. B 78, 054410 (2008)
A. Barak, O. Peleg, C. Stucchio, A. Soffer, M. Segev, Phys. Rev. Lett. 100, 153901 (2008)
T. Ernst, J. Brand, Phys. Rev. A 81, 033614 (2010)
W. Wan, S. Muenzel, J.W. Fleischer, Phys. Rev. Lett. 104, 073903 (2010)
C.P. Jisha, A. Alberucci, R.-K. Lee, G. Assanto, Opt. Lett. 36, 1848 (2011)
R.W. Hasse, Phys. Rev. A 25, 583 (1982)
M.A. de Moura, Phys. Rev. A 37, 4998 (1988)
L.E. Ballentine, Y. Yang, J.P. Zibin, Phys. Rev. A 50, 2854 (1994)
L.E. Ballentine, Quantum Mechanics: a Modern Development (World Scientific, 1998)
T. Tsuzuki, J. Low Temp. Phys. 4, 441 (1971)
L.P. Pitaevskii, Sov. Phys. JETP 13, 451 (1961)
E.P. Gross, Nuovo Cimento 20, 454 (1961)
E. Merzbacher, Quantum Mechanics, 3rd edn. (John Wiley & Sons, 1998)
G. Pöschl, E. Teller, Z. Phys. 83, 143 (1933)
N. Rosen, P.M. Morse. Phys. Rev. 42, 210 (1932)
R.J. Glauber, Phys. Rev. 131, 2766 (1963)
E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)
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)
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)
V.N. Serkin, T.L. Belyaeva, G.H. Corro, M.A. Granados, Quantum Electron. 33, 325 (2003)
V.N. Serkin, T.L. Belyaeva, G.H. Corro, M.A. Granados, Quantum Electron. 33, 456 (2003)
C. Ramsauer, Ann. Phys. 4, 513 (1921)
V.A. Bailey, J.S. Townsend, Phil. Mag. 6, 873 (1921)
L.M. Kovachev, Opt. Express 15, 10318 (2007)
L.M. Kovachev, J. Mod. Opt. 55, 2975 (2008)
J. Leuthold, C. Foos, W. Freude, Nature Photonics 4, 535 (2010)
D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)
E. Witkowska, P. Deuar, M. Gajda, K. Rzkazewski, Phys. Rev. Lett. 106, 135301 (2011)
F. Cattani, A. Kim, D. Anderson, M. Lisak, Phys. Rev. A 83, 013608 (2011)
K. Nakamura, Z.A. Sobirov, D.U. Matrasulov, S. Sawada, Phys. Rev. E 84, 026609 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2012-30214-2