Rotational Brownian motion of a two-dimensional rigid rotator: relaxation and steady-state regimes

Abstract

Exact analytical expressions for the dielectric and Kerr functions in both relaxation and steady-state regimes are explicitly calculated by solving the Fokker–Planck–Kramers (FPK) equation for the rotational Brownian motion of a rigid rotator in 2D. The response functions which are thus obtained, generalize and extend all the results recently published on the topic. The particular case of the Debye–Smoluchowski diffusion model is straightforwardly recovered. We give also the entropy formula for the rotator system and analyse the implication of the second principle of thermodynamics for the steady-state dielectric and Kerr functions.