Circular OneDimensional Model for the ElectronIon System. I. RandomPhase Approximation
Abstract
This paper, which is first of a series about a system of "electrons" and "ions" constrained to move on a circle with an interaction potential whose Fourier transform is the inverse square of the momentum variable, applies the conventional tools of the equation of motion method in the randomphase approximation and Bardeen and Pines's canonical transformations, as well as the wellknown Cooperpair considerations. It is found that the model is in all ways similar to the threedimensional electronion system: It displays collective modes (plasmons and phonons), screening, etc., with the familiar renormalization factors. The existence of a phononmediated attraction and the Cooperpair analysis lead to the existence of bound pairs and an energy gap.
 Publication:

Physical Review
 Pub Date:
 December 1968
 DOI:
 10.1103/PhysRev.176.510
 Bibcode:
 1968PhRv..176..510C