The Green's function method and superconductivity of systems of fermions

B. L. G. Bakker, M. I. Polikarpov, A. I. Veselov

MI Imo

We present some basic Green’s functions of superconductivity, making emphasis on their geneology and analytic properties. From calculations, we note that the temperature dependence of the Green’s functions for fermionic (and bosonic) systems limits and defines the extent of their applications and results. Furthermore, the Gorkov interaction term of the four field fermion operators, is examined and interpreted in terms of the Landau condensate. Finally we show that the Gorkov interaction under a certain condition sustains superconductivity and spin density wave in the system.KEYWORDS: Green’s functions, Bethe-Salpeter equation, Landau condensate, superconductivity, spin density wave.

Victor Nikolaevich Popov

Alexandre M. Zagoskin

B. L. G. Bakker, M. I. Polikarpov, A. I. Veselov

The time evolution of a many-fermion system can be described by a Green's function corresponding to an effective potential, which takes anti-symmetrization of the wave function into account, called the Pauli-potential. We show that this idea can be combined with the Green's Function Monte Carlo method to accurately simulate a system of many non-relativistic fermions. The method is illustrated by the example of systems of several (2-9) fermions in a square well.

Philippe A. Martin, FRANÇOIS ROTHEN