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Quasiparticle projection method for dynamically unstable Bose-Einstein condensates

Asier Izquierdo1,2, Maria Arazo2,3,*, Sofía Martínez-Garaot1,2, and Michele Modugno2,3,4

  • *Contact atuhor: maria.arazo@ehu.eus
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APS Open Sci. 1, 000043 – Published 18 June, 2026

DOI: https://doi.org/10.1103/pnh7-f3v9

Abstract

We present a general formalism for performing a time-dependent Bogoliubov analysis of a dynamically unstable Bose-Einstein condensate, which extends the quasiparticle projection method of Morgan et al. [Phys. Rev. A 57, 3818 (1998)] to cases with a complex spectrum. By introducing the proper left eigenvectors associated with each regime, we construct a biorthogonal basis. While the usual Bogoliubov normalization 〈u|u〉−〈v|v〉=1 may not hold in this basis, it still allows for a complete mode decomposition and an accurate reconstruction of arbitrary perturbations over time. This approach extends the applicability of the Bogoliubov framework beyond the stable regime, providing a consistent analysis of the time evolution of unstable condensates. As a proof of concept, we apply the method to a one-dimensional condensate with attractive interactions, which is dynamically unstable and evolves into nonstationary localized structures seeded by small perturbations. Overall, the present method provides a complete and robust mode expansion that remains meaningful beyond the linear regime and useful for characterizing the macroscopic development of instabilities.

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References (32)

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APS Open Sci. 1, 000043– Published 18 June, 2026
Vol. 1
  • Received 16 December 2025
  • Revised 8 May 2026
  • Accepted 8 June 2026
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