JP Journal of Algebra, Number Theory and Applications
Volume 11, Issue 2, Pages 137 - 158
(August 2008)
|
|
SUPERCONDUCTIVITY AND THE BCS-BOGOLIUBOV THEORY
Shuji Watanabe (Japan)
|
Abstract: First, we reformulate the BCS-Bogoliubov theory of superconductivity from the viewpoint of linear algebra. We define the BCS Hamiltonian on where M is a positive integer. We discuss selfadjointness and symmetry of the BCS Hamiltonian as well as spontaneous symmetry breaking. Beginning with the gap equation, we give the well-known expression for the BCS state and find the existence of an energy gap.We also show that the BCS state has a lower energy than the normal state. Second, we introduce a new superconducting state explicitly and show from the viewpoint of linear algebra that this new state has a lower energy than the BCS state. Third, beginning with our new gap equation, we show from the viewpoint of linear algebra that we arriveat the results similar to those in the BCS-Bogoliubov theory. |
Keywords and phrases: superconductivity, the BCS-Bogoliubov theory, new superconducting state having a lower energy than the BCS state, new gap equation. |
|
Number of Downloads: 441 | Number of Views: 1191 |
|