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.

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• Holographic dissipative space-time supersolids
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• Dynamical instabilities and quasi-normal modes, a spectral analysis with applications to black-hole physics
• Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
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• Unifying treatment of nonequilibrium and unstable dynamics of cold bosonic atom system with time-dependent order parameter in Thermo Filed Dynamics
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• Analytical study on parameter regions of dynamical instability for two-component Bose--Einstein condensates with coaxial quantized vortices
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