A practical course on quantum Monte Carlo Vesa Apaja

Format:

Book

Author/Creator:

Apaja, Vesa, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP series in quantum technology

Language:

English

Subjects (All):

Quantum Monte Carlo methods.

Physical Description:

1 online resource

Edition:

1st ed.

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) IOP Publishing [2025]

Biography/History:

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

Summary:

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. Part of IOP Series in Quantum Technology

Contents:

1. Introduction

1.1. The Schrödinger equation

1.2. Indistinguishable particles and the ground state

1.3. Solving quantum problems with Monte Carlo

2. Variational Monte Carlo (VMC)

2.1. Spin in expectation values

2.2. The multielectron wave function

2.3. The Jastrow factor

3. Principles of wave function optimization

3.1. Energy and variance optimization

3.2. Direct and correlated sampling

3.3. He atom : energy and variance optimization

4. Diffusion Monte Carlo

4.1. Projection on the ground state

4.2. Imaginary-time Schrödinger equation

4.3. Stochastic representation of a wave function

4.4. Importance sampling DMC

4.5. Case study : importance sampling DMC for a particle in a box

4.6. Case study : DMC for a particle in a box without importance sampling

4.7. DMC for bosons and fermions

4.8. Fixed-node DMC of atoms and small molecules

5. Path integral Monte Carlo

5.1. From real-time path integrals to imaginary-time path integrals

5.2. High-temperature density matrix

5.3. Path generation

5.4. Worm algorithm and permutation sampling

5.5. Approximate action

5.6. PIMC measurements

5.7. Practical suggestions for testing a PIMC code

5.8. Stochastic series expansion

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

Notes:

"Version: 20250801"--Title page verso

Includes bibliographical references

Online resource; title from PDF title page (viewed on September 5, 2025)

Other Format:

Print version A practical course on quantum Monte Carlo

ISBN:

9780750363105

9780750363099

OCLC:

1535209519

Access Restriction:

Restricted for use by site license