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

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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.

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Correspondence to Daniel Haag.

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Haag, D., Dast, D., Cartarius, H. et al. Finite element Calculations of \(\mathcal {P}\mathcal {T}\)-Symmetric Bose-Einstein Condensates. Int J Theor Phys 54, 4100–4109 (2015). https://doi.org/10.1007/s10773-014-2481-2

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Keywords

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