Quasiparticle projection method for dynamically unstable Bose-Einstein condensates
This work develops a method to analyze unstable Bose-Einstein condensates using a time-dependent Bogoliubov expansion. It uses biorthogonal bases to handle complex excitation spectra, allowing for accurate reconstruction of the system's state beyond the linear regime. The approach tracks how instabilities grow and mix modes, showing how weak initial perturbations evolve into macroscopic structures.