Condition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations

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dc.creatorNakamura, Y.
dc.creatorMine, M.
dc.creatorOkumura, M.
dc.creatorYamanaka, Y.
dc.date2008-01-21
dc.date2008-04-04
dc.date.accessioned2026-07-07T09:30:01Z
dc.date.available2026-07-07T09:30:01Z
dc.descriptionThe condition for the appearance of dynamical instability of the Bose-condensed system, characterized by the emergence of complex eigenvalues in the Bogoliubov-de Gennes equations, is studied analytically. We perturbatively expand both the Gross-Pitaevskii and Bogoliubov-de Gennes equations with respect to the coupling constant. It is concluded that the degeneracy between a positive-norm eigenmode and a negative-norm one is essential for the emergence of complex modes. Based on the conclusion, we justify the two-mode approximation applied in our previous work [E. Fukuyama \textit{et al}., Phys. Rev. A {\bf 76}, 043608 (2007)], in which we analytically studied the condition for the existence of complex modes when the condensate has a highly quantized vortex.
dc.description7pages
dc.identifierhttps://arxiv.org/abs/0801.3137
dc.identifierhttp://arxiv.org/abs/0801.3137
dc.identifierPhys. Rev. A 77, 043601 (2008)
dc.identifierdoi:10.1103/PhysRevA.77.043601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157998
dc.subjectOther Condensed Matter
dc.titleCondition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations
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