Use of the Sumudu transform to extract response functions from Quantum Monte Carlo calculations

We review an ab-initio method for calculating the dynamical structure function of an interacting many-body quantum system. The method consists in coupling a generalized integral transform approach with imaginary time Quantum Monte Carlo calculations. The strength of the method has been tested on the excitation spectrum of bulk atomic 4He. The peculiar form of the kernel as a representation of the delta-function has allowed to minimize the ill-posedness of the integral transform inversion. In fact it has been possible to obtain, at a considerable degree of reliability, both position and width of the collective excitations in the maxon-roton region, as well as the second collective peak. What we stress here is the ability of such a 4-function-like kernel, for which one can control position and width, to maintain in the transformed space the characteristics of the collective structures. The application to the coherent and incoherent density excitation spectrum of liquid 4He is discussed.