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Covering topics including diffusion Monte Carlo, path integral Monte Carlo, variational Monte Carlo, and fermionic complexities (and many more), this book isn't merely a compendium of methods—it's a voyage of understanding. The book empowers readers to decipher the inner workings of Quantum Monte Carlo. It doesn't stop at equipping you with theories; it arms you with practical insights through sample codes, enabling you to deconstruct, analyze, and enhance existing algorithms. Ultimately, it showcases that Quantum Monte Carlo isn't just a numerical tool—it's an expedition that reveals the hidden facets of the quantum world.
Key Features:
- Accompanying code and worked examples of how an algorithm can be coded and tested
- What makes Quantum Monte Carlo superior and just as importantly, what breaks it
- Teaches statistical physics and quantum physics in parallel
- Includes detailed mathematical derivations that won’t leave blind spots
- Emphasises Quantum Monte Carlo as a tool of visualizing quantum mechanics
Vesa Apaja is a seasoned theoretical physicist, especially interested in quantum many body physics and computational physics. His first research topic was quantum fluids as a research assistant in the Department of Physics at the University of Oulu from 1990 to 1999. During that time he realised the importance of the computational approach to many body physics and wrote his first Quantum Monte Carlo codes.
In 1999, he ventured to Austria, where he joined the Many-Body Theory group at the Institut für Theoretische Physik, Johannes Kepler Universität, Linz. As a Universitäts Assistent, he expanded his research horizons to excitations in quantum fluids, and intricacies of diagrammatic many-body theory and statistical physics. In 2006, he joined the Department of Physics at the Nanoscience Center, University of Jyväskylä, Finland, where he continues to serve as a senior researcher to this day. His contributions in this role have been in a wide variety of condensed matter topics, such as flat band lattice dynamics and electrochemistry on surfaces using Kinetic Monte Carlo.
In recent years, teaching Statistical Physics, Efficient Numerical Programming, Numerical Applications in Physics, and Quantum Monte Carlo has taken most of his time. He also possesses proficient programming skills in Python, Julia, Fortran, and C++, which have been instrumental in designing and implementing advanced simulations and computational models to analyse complex physical systems.
Preface
Author biography
1 Introduction
2 Variational Monte Carlo (VMC)
3 Principles of wave function optimization
4 Diffusion Monte Carlo
5 Path integral Monte Carlo
6 Path integral ground-state Monte Carlo
Appendix A: Central limit theorem
Appendix B: Diffusion matrix elements
Appendix C: Rejection method
Appendix D: Updating Slater determinants
Appendix E: Path integral Monte Carlo virial estimator
Appendix F: Error estimation
Appendix G: Perturbation expansion