On the dynamics of the Holstein model from the anticontinuous limit

We consider the Holstein model describing an electron interacting with a la ttice of identical oscillators. We remark that the on site system (i.e., th e system in which the interaction between the different sites of the lattic e vanishes) is integrable and anisocronous. This allows us to apply some re cent Nekhoroshev-type results to show that corresponding to the majority of initial data in which the electron probability is concentrated on a finite number of sites, the electron probability distribution is approximatively constant for times growing exponentially with the inverse of the coupling p arameter. Moreover, for the same times, the total energy of the oscillator system is approximatively constant. (C) 1999 American Institute of Physics. [S0022-2488(99)00308-4].