Susceptibilities for the brownian motion in a cosine potential with application to the rotation of a dipole in a constant external field

Abstract

The susceptibility for the brownian motion in a cosine potential is proportional to the one sided Fourier transform of the velocity autocorrelation function whereas the polarizability for the rotation of a dipole in a constant external field is proportional to the one sided Fourier transform of the time derivative of the sin- and cos-autocorrelation function. The one sided Fourier transform of these autocorrelation functions can be expressed by matrix continued fractions. They are evaluated for large, medium and even for very small damping constants, thus obtaining various susceptibilities practically in the whole region of friction constants. Furthermore the connection to the zero friction limit case is discussed.