ISSN:
1434-6036
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider the Dyson equation associated with the BCS superconducting state from a mathematical point of view. The Dyson equation gives rise to a modified gap equation that is similar to the BCS gap equation, but with a different kernel. We first show that for strong coupling (such that the McMillan parameter |λ|≫1) both the real and imaginary parts of the solution Δ(E) of the modified gap equation alternate in sign as function of the excitation energyE, the periods $$\tilde \omega $$ being 4ω0 for positive λ and 4ω0/3 for negative λ. (ω0 is the frequency of an Einstein spectrum of phonons). A closed, algebraic approximation to Δ(E) is 2|λ|ω0log[cotan(πE/ $$\tilde \omega $$ )]. Finally, the poles of the kernel of the integral equation are located in the complex-E plane. For the new-type, oscillatory solution of the modified gap equation the analogue of the causal (zero-temperature) Green's function is shown to have different analytic properties from those of the smooth Eliashberg solution of BCS theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01390823
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