Thesis Overview

Chapter 2 starts with a review of the path integral Monte Carlo method that will be used throughout this work. Chapter 3 introduces a new variational principle in order to derive a variational density matrix that will be employed for a variational calculation of hydrogen and used to construct the nodal surfaces in PIMC. In chapter , we present thermodynamic properties including energy, pressure, and pair-correlation functions from PIMC simulation of hydrogen and deuterium. We discuss the high temperature phase diagram including the regime of the hypothetical plasma phase transition. Additionally, a hugoniot function will be derived and compared with recent laser shock wave experiments. Chapter 5 presents the calculation of off-diagonal density matrix elements, which requires the sampling of open paths. After a description on how this method can be applied to fermionic systems, the momentum distribution for the electron gas and for the electrons in hydrogen is discussed, which is followed by an introduction to natural orbitals. Chapter 6 presents the conclusion.