Quantum Theory of Dielectric Relaxation

The statistical behavior of a system coupled to a reservoir at temperature $T$ is discussed, with the assumption that the interactions are impulsive. Kinetic equations are written for the classical distribution function and quantum density operator. The class of operators admitted leads to a proper description of the irreversible behavior of the system, but the construction of the collision operator for a given Hamiltonian of system and reservoir is not treated. Application is made to the quantum theory of dielectric relaxation, with the further assumption that the position coordinates of the system are unchanged by collisions. An explicit solution is found for the behavior in an external alternating field, of a two-dimensional dipole of moment of inertia $I$, subject to strong collisions with the reservoir. For low collision frequency $\frac{1}{\tau }$, discrete rotational lines of width $\frac{1}{\tau }$ are found, while at high collision frequencies there is a continuous Debye spectrum with relaxation time ${\tau }^{*}=\frac{\left(\frac{1}{\tau }\right)}{\left(\frac{I}{\mathrm{kT}}\right)}$. At intermediate collision times, the absorption and dispersion are governed by an interplay of quantum and inertial effects.