New second branch of the spectrum of the BCS Hamiltonian and a “pseudogap”

• Дата: 2005
• Автор: Petrina, D.Ya.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2005
• Назва видання: Український математичний журнал
• Теми: Статті
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/165899
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: New second branch of the spectrum of the BCS Hamiltonian and a “pseudogap” / D.Ya. Petrina // Український математичний журнал. — 2005. — Т. 57, № 11. — С. 1508–1533. — Бібліогр.: 17 назв. — англ.

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.”