Levy flights in Landau-Teller model of molecular collision

We consider the Landau--Teller model, which is a prototype for the exchanges of energy, in molecular collisions, between internal degrees of freedom and those of the center of mass. We show that the statistics of the energy exchanges computed through the dynamics over a finite time is of the L'evy type for high enough frequencies of the internal motions, while it reduces to the familiar gaussian one in the limit of low frequencies. The relevance for the definition of the times of relaxation to equilibrium is also pointed out.