New second branch of the spectrum of the BCS Hamiltonian and a “pseudogap”
The BCS Hamiltonian of superconductivity has the second branch of eigenvalues and eigenvectors. It consists of wave functions of pairs of electrons in ground and excited states. The continuous spectrum of excited pairs is separated by a nonzero gap from the point of the discrete spectrum that corres...
Збережено в:
| Дата: | 2005 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2005
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3704 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | The BCS Hamiltonian of superconductivity has the second branch of eigenvalues and eigenvectors. It consists of wave functions of pairs of electrons in ground and excited states. The continuous spectrum of excited pairs is separated by a nonzero gap from the point of the discrete spectrum that corresponds to the pair in the ground state. The corresponding grand partition function and free energy are exactly calculated. This implies that, for low temperatures, the system is in the condensate of pairs in the ground state. The sequence of correlation functions is exactly calculated in the thermodynamic limit, and it coincides with the corresponding sequence of the system with approximating Hamiltonian. The gap in the spectrum of excitations depends continuously on temperature and is different from zero above the critical temperature corresponding to the first branch of the spectrum. In our opinion, this fact explains the phenomenon of “pseudogap.” |
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