A QUANTUM-STATISTICAL MODEL OF A 3-DIMENSIONAL LINEAR RIGID ROTATOR IN A BATH OF OSCILLATORS .3. DC FIELD DIELECTRIC PROPERTY DYNAMICS

With the aid of a recently derived master equation, which for commodit y purposes will be referred to as the Haunkonnou-Navez master equation , the dielectric properties of a polar fluid in a constant electric fi eld regime is analysed by studying the rotational motions of the syste m of molecules of the dielectric medium which are assimilated to linea r rigid rotators. Master equations are given for well defined matrix e lements sigma(l,l+1)(t), phi(l,l)(t) and eta(l,l+2)(t). While the elec trical susceptibility describes low-energy rotational transitions, the Kerr effect involves both low-and higher-energy transitions. For the quantum electrical susceptibility, the linear response limit is consid ered while the Kerr effect accounts for higher-order electric field ef fects. The classical Brownian limit of the quantum equations recover m ost results published to date. The convergence of the classical result s (which are. in the form of continued fractions) are guaranteed for l arge friction and/or small inertia; and low frequencies. Quantum expre ssions, valid for weak coupling (small friction and/or large inertia) are obtained via a rigorous mathematical theorem on weak coupling. The y are the Van Vleck-Weisskopf line forms for the electrical susceptibi lity and the Kerr function. More importantly, explicit expressions are given for the frequency shifts and line widths. We demonstrate the tr ansition from quantum to classical effects as the the friction/inertia parameter (zeta/I) increases. A temperature-dependent cross-over is f ound.