Ab-initio microscopic studies of elementary excitations in quantum fluids and gases

I will present results on ab--initio estimations of the dynamic structure factor in a variety of quantum systems which include quantum gases\cite{uno}, bulk $^4$He in 3D\cite{due,tre}, 2D\cite{quattro} and 1D, but also $^4$He adsorbed on graphene derivatives\cite{sei, sette}. The dynamic structure factors have been extracted from imaginary--time correlation functions, computed via a Path Integral projector method, by using the Genetic Inversion via Falsification of Theories (GIFT) method\cite{due}. In the gas phase we have used the hard--sphere potential to model the two--body interaction between the atoms. By changing the gas parameter from the dilute regime up to densities above the freezing point of the hard--sphere system we observe the emergence of a broad multiphonon contribution accompanying the quasi--particle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov--like spectrum to a phonon--maxon--roton curve. In 2D $^4$He we have explored the full density range from the region of spinodal decomposition to the freezing density. As the density increases, the dispersion at low wave vectors changes from a superlinear (anomalous dispersion) trend to a sublinear (normal dispersion) one, anticipating the crystallization of the system; at the same time the maxon-–roton structure, which is barely visible at low density, becomes well developed at high densities and the roton wave vector has a strong density dependence. We have studied also the elementary excitation spectrum of quasi--2D anisotropic superfluids: $^4$He adsorbed on graphene–-fluoride and graphane. We found a phonon-–maxon-–roton dispersion relation that is strongly anisotropic in the roton region for the graphene–-fluoride case. New results about elementary excitations in 1D $^4$He will be also discussed.