Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states. Matsumoto, H. & Sakamoto, S. Progress of Theoretical Physics, 107(4):679–688, 2002.
Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states [link]Paper  doi  abstract   bibtex   
In Bose-Einstein condensation of dilute alkaline atomic gases, a magnetic trapped potential forces particle-excitation levels to have a discrete spectrum. This indicates that there must arise a discrete zero-mode associated with the phase symmetry to be consistent with the Goldstone theorem. It is shown that the zero-mode can be identified as a quantum phase coordinate and that its presence is required from the canonical relation of field operators. Thermal fluctuations of the quantum phase coordinate induce a T log Nc3/5T term in the free energy and a kBTNc-2/5 term in the particle number, where Nc is the number of condensed particles.
@article{matsumoto_quantum_2002,
abstract = {In Bose-Einstein condensation of dilute alkaline atomic gases, a magnetic trapped potential forces particle-excitation levels to have a discrete spectrum. This indicates that there must arise a discrete zero-mode associated with the phase symmetry to be consistent with the Goldstone theorem. It is shown that the zero-mode can be identified as a quantum phase coordinate and that its presence is required from the canonical relation of field operators. Thermal fluctuations of the quantum phase coordinate induce a T log Nc3/5T term in the free energy and a kBTNc-2/5 term in the particle number, where Nc is the number of condensed particles.},
annote = {From Duplicate 2 (Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states - Matsumoto, Hideki; Sakamoto, Shoichi)

Publisher: Progress of Theoretical Physics},
author = {Matsumoto, Hideki and Sakamoto, Shoichi},
doi = {10.1143/PTP.107.679},
issn = {0033068X},
journal = {Progress of Theoretical Physics},
number = {4},
pages = {679--688},
title = {{Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states}},
url = {http://ptp.ipap.jp/link?PTP/107/679/},
volume = {107},
year = {2002}
}

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