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

Y. Nakamura; M. Mine; M. Okumura; Y. Yamanaka

doi:10.1103/PhysRevA.77.043601

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

Y. Nakamura^*, M. Mine, M. Okumura, Y. Yamanaka

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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. 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, in which we analytically studied the condition for the existence of complex modes when the condensate has a highly quantized vortex.

Original language	English
Article number	043601
Journal	Physical Review A - Atomic, Molecular, and Optical Physics
Volume	77
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevA.77.043601
Publication status	Published - 2008 Apr 1

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics

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10.1103/PhysRevA.77.043601

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title = "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. 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, 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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T1 - Condition for emergence of complex eigenvalues in the Bogoliubov-de Gennes equations

AU - Nakamura, Y.

AU - Mine, M.

AU - Okumura, M.

AU - Yamanaka, Y.

PY - 2008/4/1

Y1 - 2008/4/1

N2 - 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. 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, in which we analytically studied the condition for the existence of complex modes when the condensate has a highly quantized vortex.

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

Abstract

ASJC Scopus subject areas

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