Kubo Lineshape and its Fitted q-Gaussian Tsallis Function

Here we consider the Kubo lineshape, that is the Fourier transform of Kubo stochastic time-correlation function, and its fitted q-Gaussian function. In particular we investigate how q-Tsallis Gaussian functions can be used as a substitute of a Kubo lineshape. In fact, the q-Gaussian has a simple analytic expression, whereas the Kubo lineshape requires a numerical calculation of Fourier transform. The aim of this investigation is to further generalize the application of q-Gaussian Tsallis functions in Raman spectroscopy.