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].