Thermally activated escape rate for the Brownian motion of a fixed axis rotator in a double well potential for all values of the dissipation

Abstract

The rotational Brownian motion of fixed axis rotators in a double well cosine potential was analyzed using the extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping. The procedure yielded an expression for the Kramers escape rate valid for all values of the dissipation including, crossover regimes, very low damping (VLD) and very high damping (VHD). It was shown that this equation provided a good asymptotic estimate of the correlation time of the longitudinal dipole moment correlation function. For low barriers, analytic equations for correlation time in the VLD and VHD limits were derived.