FM 21-05; cond-mat/0507686

Authors: Vieri Mastropietro

Title Gap generation in the BCS model with finite range time dependent interaction

Abstract: In the [BCS] paper the theory of superconductivity was developed for the BCS model, in which the (instantaneous) interaction is only between fermions of opposite momentum and spin. Such model was analyzed by variational methods, finding that a superconducting behavior is energetically favorable. Subsequently it was claimed that in the thermodynamic limit the BCS model is equivalent to the (exactly solvable) quadratic mean field BCS model; a rigorous proof of this claim is however still lacking. In this paper we consider the BCS model with a finite range time dependent interaction, and we prove rigorously its equivalence with the mean field BCS model in the thermodynamic limit if the range is long enough, by a (uniformly convergent) perturbation expansion about mean field theory.

Key words:  BCS model, Superconductivity

Vieri Mastropietro
Matematica, Universita' di Roma 2
V.le della Ricerca Scientifica
00133 Roma, Italia
tel +39-06-7259-4209