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

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.

7pages

References in corpus (7)

• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Splitting Instability of a Multiply Charged Vortex in a Bose-Einstein Condensate
• Complex modes in unstable quadratic bosonic forms
• Stability analysis for $n$-component Bose-Einstein condensate
• Quantum Field Theoretical Description of Unstable Behavior of Trapped Bose-Einstein Condensates with Complex Eigenvalues of Bogoliubov-de Gennes Equations
• Condition for the Existence of Complex Modes in a Trapped Bose--Einstein Condensate with a Highly Quantized Vortex

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