The Green function of degenerate systems

Christian Brouder (1) , Gianluca Panati (2) , Gabriel Stoltz (3)

1 IMPMC - Institut de minéralogie et de physique des milieux condensés
2 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of $H_0$ leading to eigenstates of $H_0+V$ for degenerate systems. These initial states are eigenstates of $P_0 V P_0$, where $P_0$ is the projection onto a degenerate eigenspace of $H_0$. This result is used to give the proper definition of the Green function, the statistical Green function and the non-equilibrium Green function of degenerate systems. The convergence of these Green functions is established.

Mots clés: Green's functions; adiabatic approximation; degenerate systems

Domaines: Electrons fortement corrélés [cond-mat.str-el]; Physique mathématique [math-ph]

Christian Brouder, Gianluca Panati, Gabriel Stoltz. The Green function of degenerate systems. 2009. ⟨hal-00394238v1⟩