Projected Gross–Pitaevskii Equation for Ring-Shaped Bose–Einstein Condensates


  • O.O. Prikhodko Taras Shevchenko National University of Kyiv, Department of Physics
  • Y.M. Bidasyuk Physikalisch-Technische Bundesanstalt



Bose–Einstein condensation, Gross–Pitaevskii equation, spectral methods


We propose an alternative implementation of the projected Gross–Pitaevskki equation adapted for a numerical modeling of the atomic Bose–Einstein condensate trapped in a toroidally shaped potential. We present an accurate efficient scheme to evaluate the required matrix elements and to calculate tthe ime evolution of the matter wave field. We analyze the stability and accuracy of the developed method for equilibrium and nonequilibrium solutions in a ring-shaped trap with an additional barrier potential corresponding to recent experimental realizations.


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How to Cite

Prikhodko, O., & Bidasyuk, Y. (2021). Projected Gross–Pitaevskii Equation for Ring-Shaped Bose–Einstein Condensates. Ukrainian Journal of Physics, 66(3), 198.



Optics, atoms and molecules