Non-exponential time-correlation function for random physical processes

TL;DR

This paper introduces a new correlation function that corrects the theoretical inaccuracies of the exponential form in linear response processes, providing better data fitting and mathematical consistency across all relevant frequency ranges.

Contribution

A novel correlation function is proposed that overcomes the limitations of the exponential model, applicable to all processes described by linear response theory.

Findings

Fits dielectric relaxation data better than exponential function

The new function is consistent across all frequency ranges

Mathematically superior to the exponential correlation function

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.