International Journal of Theoretical Physics

, Volume 54, Issue 11, pp 4100–4109

Finite element Calculations of \(\mathcal {P}\mathcal {T}\)-Symmetric Bose-Einstein Condensates

  • Daniel Haag
  • Dennis Dast
  • Holger Cartarius
  • Günter Wunner
Article

DOI: 10.1007/s10773-014-2481-2

Cite this article as:
Haag, D., Dast, D., Cartarius, H. et al. Int J Theor Phys (2015) 54: 4100. doi:10.1007/s10773-014-2481-2
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Abstract

\(\mathcal {P}\mathcal {T}\)-symmetric systems have been intensively studied in optical waveguides, where the \(\mathcal {P}\mathcal {T}\) symmetry is achieved by pumping and absorption processes. In such systems the \(\mathcal {P}\mathcal {T}\) symmetry leads to a wide range of effects promising technical and scientific applications. By analogy, balanced gain and loss of particles in Bose-Einstein condensates (BEC) can be described by introducing a \(\mathcal {P}\mathcal {T}\)-symmetric imaginary potential into the Gross-Pitaevskii equation (GPE). This equation can be solved numerically by various methods including the finite element approach. We apply this method to the GPE with arbitrary complex potentials and explicitly solve a double-well potential with shifted barriers.

Keywords

Bose-Einstein condensation Finite element method \(\mathcal {P}\mathcal {T}\) symmetry 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Daniel Haag
    • 1
  • Dennis Dast
    • 1
  • Holger Cartarius
    • 1
  • Günter Wunner
    • 1
  1. 1.1. Institut für Theoretische PhysikUniversität StuttgartStuttgartGermany