A QUANTUM-STATISTICAL MODEL OF A 3-DIMENSIONAL LINEAR RIGID ROTATOR IN A BATH OF OSCILLATORS .1. ELECTRICAL SUSCEPTIBILITY DERIVATION

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, impose d by the weak-coupling assumptions, are then examined in detail. The f irst regime, corresponding to the classical Brownian limit, leads to t he same electrical susceptibility formulae as deduced from the well kn own Fokker-Planck-Kramers equation for the rotational Brownian motion. The second regime appears as the Van Hove limit for the master equati on in the interaction picture. Based on the application of a mathemati cal theorem by E B Davies, this limit provides an elegant Van Vleck-We isskopf lineform for the electrical susceptibility, explicitly express ed for the model considered here.