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]](https://bibbase.org/img/filetypes/link.svg "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}
}
Downloads: 0
{"_id":"8tu4WQW6ZbahDAJpn","bibbaseid":"matsumoto-sakamoto-quantumphasecoordinateasazeromodeinboseeinsteincondensedstates-2002","author_short":["Matsumoto, H.","Sakamoto, S."],"bibdata":{"bibtype":"article","type":"article","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":[{"propositions":[],"lastnames":["Matsumoto"],"firstnames":["Hideki"],"suffixes":[]},{"propositions":[],"lastnames":["Sakamoto"],"firstnames":["Shoichi"],"suffixes":[]}],"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","bibtex":"@article{matsumoto_quantum_2002,\nabstract = {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.},\nannote = {From Duplicate 2 (Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states - Matsumoto, Hideki; Sakamoto, Shoichi)\n\nPublisher: Progress of Theoretical Physics},\nauthor = {Matsumoto, Hideki and Sakamoto, Shoichi},\ndoi = {10.1143/PTP.107.679},\nissn = {0033068X},\njournal = {Progress of Theoretical Physics},\nnumber = {4},\npages = {679--688},\ntitle = {{Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states}},\nurl = {http://ptp.ipap.jp/link?PTP/107/679/},\nvolume = {107},\nyear = {2002}\n}\n","author_short":["Matsumoto, H.","Sakamoto, S."],"key":"matsumoto_quantum_2002","id":"matsumoto_quantum_2002","bibbaseid":"matsumoto-sakamoto-quantumphasecoordinateasazeromodeinboseeinsteincondensedstates-2002","role":"author","urls":{"Paper":"http://ptp.ipap.jp/link?PTP/107/679/"},"metadata":{"authorlinks":{}}},"bibtype":"article","biburl":"https://cloud.swalk.xyz/bebop/bibtex.bib","dataSources":["7fTi5NtYYKwjPXfpu"],"keywords":[],"search_terms":["quantum","phase","coordinate","zero","mode","bose","einstein","condensed","states","matsumoto","sakamoto"],"title":"Quantum phase coordinate as a zero-mode in Bose-Einstein condensed states","year":2002}