DYNAMICAL PROPERTIES OF MANY--BODY SYSTEMS FROM CONFIGURATIONAL AND DETERMINANTAL QUANTUM MONTE CARLO METHODS.

The numerical simulation of quantum many-body systems is an essential instrument in the research on condensed matter Physics. Recent years have witnessed remarkable progress in studying dynamical properties of non-relativistic Bose systems with quantum Monte Carlo (QMC) methods. On the other hand, the numerical study of Fermi systems is a still open problem of great relevance, as fermions constitute a substantial part of ordinary matter and methods for the accurate calculation of their ground-state and dynamical properties would be useful instruments for the interpretation of experimental data. In this thesis, a number of approximate schemes for studying ground-state and dynamical properties of quantum many-body systems are presented and employed to calculate ground-state and dynamical properties of Bose and Fermi systems. In particular, the Path Integral Ground State QMC method is used to investigate density fluctuations in one-dimensional systems of Helium atoms and hard rods, and the phaseless Auxiliary field QMC is used to investigate the electronic band and effective mass of the two-dimensional homogeneous electron gas.