Relaxation rate distribution and decay profile : one fracton emission

The relaxation rate of a localized electronic state interacting with localized vibrational states (fractons, localized phonons) is calculated for the one-vibrational quantum case. Care is taken to deal with the statistics of finding the localized vibration of appropriate energy position which can relax a given electronic state. The one quantum relaxation rate probability distribution is calculated. The time dependence of the relaxation profile is slower than exponential, but faster than any power law Calcul du taux de relaxation d'un etat electronique localise interagissant avec des etats vibrationnels localises (fractons, phonons localises) pour le cas a un quantum de vibration. Etude detaillee de la statistique des etats vibrationnels, d'energie et position appropriees, qui peuvent participer a la relaxation d'un etat electronique donne. Calcul de la distribution de probabilite du taux de relaxation a un quantum. Obtention d'une variation temporelle du profil de relaxation plus lente qu'une decroissance exponentielle, mais plus rapide que toute decroissance en loi de puissance