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arXiv · 0801.3137

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

Y. Nakamura·M. Mine·M. Okumura·Y. Yamanaka
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Abstract

The 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.

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Y. Nakamura, M. Mine, M. Okumura, Y. Yamanaka. 2008-04-04. Condition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations. https://doi.org/10.1103/physreva.77.043601

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