Contents

• Introduction
  • The High-Temperature Phase Diagram
  • Astrophysical Relevance
  • Experimental Applications
  • Free Energy Models
  • Computational Methods
  • Units
  • Thesis Overview
  
  
• Path Integral Monte Carlo Method
  • The Thermal Density Matrix
  • Imaginary Time Path Integrals
  • Pair Density Matrix
    • Short Range Action
    • Long Range Action
  • Path Integrals for Fermions and Bosons
  • Monte Carlo Sampling
    • Metropolis Monte Carlo
    • Single Slice Moves
    • Multilevel Moves
    • Permutation Sampling
  • Fermion Nodes
    • Fermion Sign Problem
    • Restricted Path Integrals
    • Trial Density Matrix
    • The Reference Point
    • Example: Nodes for Two Particles
    • Nodal Action
    • Improvements in the Nodal Action
    • Distribution of Permutation Cycles
    • Sampling Procedure
  
  
• Variational Density Matrix Technique
  • Analogy to Zero Temperature Methods
  • Variational Principle for the Many Body Density Matrix
  • Analogy to Real-Time Wave Packet Molecular Dynamics
  • Example: Particle in an External Field
  • Variational Density Matrix Properties
    • Zero Temperature Limit
    • Loss of Symmetry
    • Thermodynamic Estimators
  • Variational Many-Particle Density Matrix
  • Antisymmetry in the Parameter Equations
  • Results from Many-Particle Simulations
  • Extensions of the Gaussian Ansatz
  
  
• Thermodynamic Properties of Dense Hydrogen
  • Accuracy of the Pair Density Matrix
  • Phase Diagram
  • Comparison of Variational and Free Particle Nodes
  • Pair Correlation Functions
  • Equation of State
  • Shock Hugoniot
  
  
• Off-Diagonal Density Matrix Elements
  • Sampling with Open Paths
  • Nodal Restriction for Open Paths
  • Momentum Distribution
  • Natural orbitals
    • Motivation
    • Example: One Hydrogen Atom
    • Many-Particle Systems
  
  
• Conclusions
• Variational Interaction Terms
• Finite Temperature Jastrow Factor
• Debye Model
• Equation of State Tables
• Bibliography