A quantum statistical model of a three-dimensional linear rigid rotator in a bath of oscillators. I. Electrical susceptibility derivation
Patrick Navez, Mahouton Norbert Hounkonnou
We consider a model Hamiltonian describing a rotor as fixed and weakly interacting with a bath of oscillators. From the basic principles of statistical mechanics, we derive the corresponding master equation for the rotor density matrix operator. Two relevant limit regimes, imposed by the weak-coupling assumptions, are then examined in detail. The first regime, corresponding to the classical Brownian limit, leads to the same electrical susceptibility formulae as deduced from the well known Fokker-Planck-Kramers equation for the rotational Brownian motion. The second regime appears as the Van Hove limit for the master equation in the interaction picture. Based on the application of a mathematical theorem by E.B. Davies (1976), this limit provides an elegant Van Vleck-Weisskopf lineform for the electrical susceptibility, explicitly expressed for the model considered here.
Journal of Physics A Mathematical and General•Nov 21, 1995•6 citations