Phase invariant perturbation scheme in Bose-Einstein condensed states. Matsumoto, H. & Sakamoto, S. Progress of Theoretical Physics, 107(4):689–702, 2002.
Phase invariant perturbation scheme in Bose-Einstein condensed states [link]Paper  doi  abstract   bibtex   
In the Bose-Einstein condensation of a dilute alkaline atomic gas trapped in a magnetic potential, one has to deal with a strongly space- (and time-) dependent order parameter, which violates the phase symmetry. In this case, certain relations are required among propagators and vertices, known as Ward-Takahashi identities. In this paper, we show that a systematic self-consistent perturbation scheme can be developed even with a space-time order parameter in such a way as to satisfy the requirement of phase symmetry. The key procedure is that the information concerning the full order parameter, which is self-consistently determined, is included in the unperturbed Hamiltonian.
@article{matsumoto_phase_2002,
abstract = {In the Bose-Einstein condensation of a dilute alkaline atomic gas trapped in a magnetic potential, one has to deal with a strongly space- (and time-) dependent order parameter, which violates the phase symmetry. In this case, certain relations are required among propagators and vertices, known as Ward-Takahashi identities. In this paper, we show that a systematic self-consistent perturbation scheme can be developed even with a space-time order parameter in such a way as to satisfy the requirement of phase symmetry. The key procedure is that the information concerning the full order parameter, which is self-consistently determined, is included in the unperturbed Hamiltonian.},
annote = {From Duplicate 1 (Phase invariant perturbation scheme in Bose-Einstein condensed states - Matsumoto, Hideki; Sakamoto, Shoichi)

Publisher: Progress of Theoretical Physics},
author = {Matsumoto, Hideki and Sakamoto, Shoichi},
doi = {10.1143/PTP.107.689},
issn = {0033068X},
journal = {Progress of Theoretical Physics},
number = {4},
pages = {689--702},
title = {{Phase invariant perturbation scheme in Bose-Einstein condensed states}},
url = {http://ptp.ipap.jp/link?PTP/107/689/},
volume = {107},
year = {2002}
}

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