Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space
Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermion...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146617 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space / Yan-Gang Miao, H. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862558203176288256 |
|---|---|
| author | Miao, Yan-Gang Wang, H. |
| author_facet | Miao, Yan-Gang Wang, H. |
| citation_txt | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space / Yan-Gang Miao, H. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the noncommutative space can be described in terms of the ordinary creation and annihilation operators related to the commutative space, while the noncommutative effect appears only in the coefficients of the interacting Hamiltonian. As a result, we can rigorously solve the energy spectrum of the Fermi gas on the noncommutative space exactly following the way adopted on the commutative space without the use of perturbation theory. In particular, different from the previous results on the noncommutative degenerate electron gas and superconductor where only the first order corrections of the ground state energy level and energy gap were derived, we obtain the nonperturbative energy spectrum for the noncommutative superfluid Fermi gas, and find that each energy level contains a corrected factor of cosine function of noncommutative parameters. In addition, our result shows that the energy gap becomes narrow and the critical temperature of phase transition from a superfluid state to an ordinary fluid state decreases when compared with that in the commutative case.
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| first_indexed | 2025-11-25T22:46:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146617 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:46:44Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Miao, Yan-Gang Wang, H. 2019-02-10T10:08:20Z 2019-02-10T10:08:20Z 2014 Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space / Yan-Gang Miao, H. Wang // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 41 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D55; 81T75; 82D55 DOI:10.3842/SIGMA.2014.075 https://nasplib.isofts.kiev.ua/handle/123456789/146617 Based on the Bogoliubov non-ideal gas model, we discuss the energy spectrum and phase transition of the superfluid Fermi gas of atoms with a weak attractive interaction on the canonical noncommutative space. Because the interaction of a BCS-type superfluid Fermi gas originates from a pair of Fermionic quasi-particles with opposite momenta and spins, the Hamiltonian of the Fermi gas on the noncommutative space can be described in terms of the ordinary creation and annihilation operators related to the commutative space, while the noncommutative effect appears only in the coefficients of the interacting Hamiltonian. As a result, we can rigorously solve the energy spectrum of the Fermi gas on the noncommutative space exactly following the way adopted on the commutative space without the use of perturbation theory. In particular, different from the previous results on the noncommutative degenerate electron gas and superconductor where only the first order corrections of the ground state energy level and energy gap were derived, we obtain the nonperturbative energy spectrum for the noncommutative superfluid Fermi gas, and find that each energy level contains a corrected factor of cosine function of noncommutative parameters. In addition, our result shows that the energy gap becomes narrow and the critical temperature of phase transition from a superfluid state to an ordinary fluid state decreases when compared with that in the commutative case. This paper is a contribution to the Special Issue on Deformations of Space-Time and its Symmetries. The
 full collection is available at http://www.emis.de/journals/SIGMA/space-time.html. 
 Y.-G. Miao would like to thank J.-X. Lu of the Interdisciplinary Center for Theoretical Study
 (ICTS), University of Science and Technology of China (USTC) for warm hospitality where part
 of the work was performed. This work was supported in part by the National Natural Science
 Foundation of China under grant No. 11175090 and by the Ministry of Education of China under
 grant No. 20120031110027. At last, the authors would like to thank the anonymous referees and
 the editor for their helpful comments that indeed improve this work greatly. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space Article published earlier |
| spellingShingle | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space Miao, Yan-Gang Wang, H. |
| title | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space |
| title_full | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space |
| title_fullStr | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space |
| title_full_unstemmed | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space |
| title_short | Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space |
| title_sort | energy spectrum and phase transition of superfluid fermi gas of atoms on noncommutative space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146617 |
| work_keys_str_mv | AT miaoyangang energyspectrumandphasetransitionofsuperfluidfermigasofatomsonnoncommutativespace AT wangh energyspectrumandphasetransitionofsuperfluidfermigasofatomsonnoncommutativespace |