A stochastic cage model for linear solutes

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Abstract
A stochastic cage model describing a linear solute reorienting under the action of a librational potential due to neighboring solvent molecules is presented. The fluctuations of the cage structure are taken into account by means of a suitable distribution of the librational frequency. Moreover, a detailed description of the cage dynamics is introduced by considering both the cage rotation and its restructuring through randomizations of the librational frequency and of the equilibrium orientation of the solute. With a suitable choice of the basis functions for the representation of the time evolution operator, the cage model can be solved numerically in order to compute different types of dynamical observables: angular momentum and orientational correlation functions, frequency dependent dielectric permittivity, and far-infrared spectra. Typical behavior of such observables in normal liquids is recovered from the cage model, thus demonstrating its capability of describing experimental observations at quite different time scales.