Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations

Makoto Mine, Masahiko Okumura, Tomoka Sunaga, Yoshiya Yamanaka

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo's linear response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation.

Original languageEnglish
Pages (from-to)2327-2349
Number of pages23
JournalAnnals of Physics
Volume322
Issue number10
DOIs
Publication statusPublished - 2007 Oct

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Bose-Einstein condensates
eigenvalues
elementary excitations
neutral atoms
condensates
density distribution
damping
perturbation
energy

Keywords

  • Bose-Einstein condensation
  • Indefinite metric
  • Instability
  • Quantized vortex
  • Quantum field theory

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations. / Mine, Makoto; Okumura, Masahiko; Sunaga, Tomoka; Yamanaka, Yoshiya.

In: Annals of Physics, Vol. 322, No. 10, 10.2007, p. 2327-2349.

Research output: Contribution to journalArticle

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