Flow Equations for Electron-Phonon Interactions

Details Flow Equations for Electron-Phonon Interactions Flow Equations for Electron-Phonon Interactions

1996-04-15

arxiv.org/abs/cond-mat/9604087v1

Physics

Condensed Matter

25 pages LATEX (use a4.sty v1.2) including 5 PostScript figures (tarred,gzipped,uuencoded)

Scientific paper

10.1016/S0550-3213(96)00521-4

A recently proposed method of continuous unitary transformations is used to eliminate the interaction between electrons and phonons. The differential equations for the couplings represent an infinitesimal formulation of a sequence of Fr\"ohlich-transformations. The two approaches are compared. Our result will turn out to be less singular than Fr\"ohlich's. Furthermore the interaction between electrons belonging to a Cooper-pair will always be attractive in our approach. Even in the case where Fr\"ohlich's transformation is not defined (Fr\"ohlich actually excluded these regions from the transformation), we obtain an elimination of the electron-phonon interaction. This is due to a sufficiently slow change of the phonon energies as a function of the flow parameter.

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