Abstract
The Bogoliubov–de Gennes equations are used for a number of theoretical works on the trapped Bose–Einstein condensates. We consider the case in which these equations have complex eigenvalues. We give the complete set including a pair of complex modes whose eigenvalues are complex conjugate to each other. The expansion of the quantum fields which represent neutral atoms in terms of the complete set brings about the operators associated with the complex modes, which are simply neither bosonic nor fermionic ones. The eigenstate of the Hamiltonian is given. Introducing the notion of the physical states, we discuss the instability of the condensates in the context of Kubo’s linear response theory.
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References
N.N. Bogoliubov, J. Phys. Mosc. 11, 23 (1947)
P.G. de Gennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966)
A.L. Fetter, Ann. Phys. 70, 67 (1972)
F. Dalfovo et al., Rev. Mod. Phys. 71, 463 (1999)
M. Möttönen et al., Phys. Rev. A 68, 023611 (2003)
Y. Kawaguchi, T. Ohmi, Phys. Rev. A 70, 043610 (2004)
R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)
Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)
H. Matsumoto, S. Sakamoto, Prog. Theor. Phys. 107, 679 (2002)
M. Lewenstein, L. You, Phys. Rev. Lett. 77, 3489 (1996)
L.J. Garay et al., Phys. Rev. Lett. 85, 4643 (2000)
L.J. Garay et al., Phys. Rev. A 63, 023611 (2001)
R. Rossignoli, A.M. Kowalski, Phys. Rev. A 72, 032101 (2005)
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Mine, M., Okumura, M., Sunaga, T. et al. Quantum Field Theoretical Description of Dynamical Instability of Trapped Bose–Einstein Condensates. J Low Temp Phys 148, 331–336 (2007). https://doi.org/10.1007/s10909-007-9393-y
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DOI: https://doi.org/10.1007/s10909-007-9393-y