2025/12/15 by Izquierdo, Asier, Arazo, Maria, Martínez-Garaot, Sofía +1
#FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2512.13847
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.