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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| Дата: | 2014 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2014
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
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irk-123456789-1466172019-02-11T01:23:44Z Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space Miao, Yan-Gang Wang, H. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146617 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Miao, Yan-Gang Wang, H. |
| spellingShingle |
Miao, Yan-Gang Wang, H. Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Miao, Yan-Gang Wang, H. |
| author_sort |
Miao, Yan-Gang |
| title |
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_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_sort |
energy spectrum and phase transition of superfluid fermi gas of atoms on noncommutative space |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146617 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT miaoyangang energyspectrumandphasetransitionofsuperfluidfermigasofatomsonnoncommutativespace AT wangh energyspectrumandphasetransitionofsuperfluidfermigasofatomsonnoncommutativespace |
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2023-05-20T17:25:14Z |
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2023-05-20T17:25:14Z |
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