Advertisement

Localised Nonlinear Modes in the PT-Symmetric Double-Delta Well Gross-Pitaevskii Equation

  • I. V. BarashenkovEmail author
  • D. A. Zezyulin
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 184)

Abstract

We construct exact localised solutions of the PT-symmetric Gross-Pitaevskii equation with an attractive cubic nonlinearity. The trapping potential has the form of two \(\delta \)-function wells, where one well loses particles while the other one is fed with atoms at an equal rate. The parameters of the constructed solutions are expressible in terms of the roots of a system of two transcendental algebraic equations. We also furnish a simple analytical treatment of the linear Schrödinger equation with the PT -symmetric double-\(\delta \) potential.

Keywords

Return Time Transcendental Equation Normalisation Constraint Nonlinear Mode Small Positive Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This contribution is a spin-off from the project on the jamming anomaly in \({ PT}\) -symmetric systems [4]; we thank Vladimir Konotop for his collaboration on the main part of the project. Nora Alexeeva’s numerical assistance and Holger Cartarius’ useful remarks are gratefully acknowledged. This work was supported by the NRF of South Africa (grants UID 85751, 86991, and 87814) and the FCT (Portugal) through the grants UID/FIS/00618/2013 and PTDC/FIS-OPT/1918/2012.

References

  1. 1.
    S. Klaiman, U. Günther, N. Moiseyev, Visualization of branch points in PT-symmetric waveguides. Phys. Rev. Lett. 101, 080402 (2008)Google Scholar
  2. 2.
    H. Cartarius, G. Wunner, Model of a PT-symmetric Bose-Einstein condensate in a \(\delta \)-function double-well potential. Phys. Rev. A 86, 013612 (2012)Google Scholar
  3. 3.
    Z.H. Musslimani, K.G. Makris, R. El-Ganainy, D.N. Christodoulides, Optical solitons in PT periodic potentials. Phys. Rev. Lett. 100, 030402 (2008)Google Scholar
  4. 4.
    I.V. Barashenkov, D.A. Zezyulin, V.V. Konotop, Jamming anomaly in PT-symmetric systems. Submitted for publication (2016)Google Scholar
  5. 5.
    Y.B. Gaididei, S.F. Mingaleev, P.L. Christiansen, Curvature-induced symmetry breaking in nonlinear Schrödinger models. Phys. Rev. E 62, R53 (2000)ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    R.K. Jackson, M.I. Weinstein, Geometric analysis of bifurcation and symmetry breaking in a Gross-Pitaevskii equation. J. Stat. Phys. 116, 881 (2004)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    M. Znojil, V. Jakubský, Solvability and PT-symmetry in a double-well model with point interactions. J. Phys. A: Math. Gen. 38, 5041 (2005)Google Scholar
  8. 8.
    V. Jakubský, M. Znojil, An explicitly solvable model of the spontaneous PT-symmetry breaking. Czechoslovak J. Phys. 55, 1113 (2005)Google Scholar
  9. 9.
    H. Uncu, E. Demiralp, Bound state solutions of the Schrödinger equation for a PT-symmetric potential with Dirac delta functions. Phys. Lett. A 359, 190 (2006)Google Scholar
  10. 10.
    H. Cartarius, D. Haag, D. Dast, G. Wunner, Nonlinear Schrödinger equation for a PT-symmetric delta-function double well. J. Phys. A: Math. Theor. 45, 444008 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.National Institute for Theoretical PhysicsStellenboschSouth Africa
  2. 2.Department of MathematicsUniversity of Cape TownCape TownSouth Africa
  3. 3.Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências da Universidade de LisboaLisbonPortugal

Personalised recommendations