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| HAL: hal-00394238, version 1 |
| arXiv: 0906.2052 |
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| Available versions: | v1 (2009-06-11) | v2 (2009-10-31) |
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| The Green function of degenerate systems |
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| Christian Brouder 1Gianluca Panati 2 |
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| (2009-06-11) |
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| 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. |
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| 1: | Institut de minéralogie et de physique des milieux condensés (IMPMC) |
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CNRS : UMR7590 – IPG PARIS – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| 2: | Dipartimento di Matematica "Guido Castelnuovo" [Roma I] |
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Universita di Roma "La Sapienza" |
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| 3: | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| Subject | : | Physics/Condensed Matter/Strongly Correlated Electrons Physics/Mathematical Physics |
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| Green's functions – adiabatic approximation – degenerate systems |
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| hal-00394238, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00394238 | |
| oai:hal.archives-ouvertes.fr:hal-00394238 | |
| From: Christian Brouder | |
| Submitted on: Thursday, 11 June 2009 09:54:44 | |
| Updated on: Thursday, 11 June 2009 10:06:49 | |
