Non-exponential time-correlation function for random physical processes

Abstract

The exponential correlation function is theoretically incorrect in the entire frequency range of interest for processes described in terms of linear response theory. The Lorentzian lineshape results from an inconsistent assumption of exponential correlation at timescales smaller than the relaxation time. A new correlation function is proposed that avoids the deficiencies of the exponential function. Comparison on dielectric relaxation in gases shows that the new correlation function can be used to fit data satisfactorily instead of the exponential function. The new correlation function is theoretically consistent for all processes described in terms of linear response theory. Its additional mathematical superiority implies that it can be used instead of the exponential function for all such processes.