2013/12/31 by J. Takahashi, Junichi Takahashi, Y. Nakamura +2
Computer Science · Physics and Astronomy · #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Eigenvalues and eigenvectors #Homogeneous space #Instability #Mathematical physics #Perturbation (astronomy) #Physics #Quantum Information and Cryptography #Quantum electrodynamics #Quantum mechanics #Strong Light-Matter Interactions #Symmetry breaking #Translational symmetry #Zero mode #cond-mat.quant-gas
paper · pdf · doi:10.1016/j.aop.2014.05.004
published as Ann. Phys. 347, 250 (2014) · 7 pages, 4 figures
openalex publication_date 2014/05/14 · arxiv created 2014/06/16 · arxiv updated 2014/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A complex eigenvalue in the Bogoliubov-de Gennes equations for a stationary Bose-Einstein condensate in ultracold atomic system indicates the dynamical instability of the system. We also have the modes with zero eigenvalues for the condensate, called the zero modes, which originate from the spontaneous breakdown of symmetries. Although the zero modes are suppressed in many theoretical analyses, we take account of them in this paper and argue that a zero mode can change into one with a pure imaginary eigenvalue by applying a symmetry breaking external perturbation potential. This emergence of a pure imaginary mode adds a new type of scenario of dynamical instability to that characterized by complex eigenvalue of the usual excitation modes. For illustration, we deal with two one-dimensional homogeneous Bose-Einstein condensate systems with a single dark soliton under a respective perturbation potential, breaking the invariance under translation, to derive pure imaginary modes.