Field Theoretic Simulations in Soft Matter and Quantum Fluids

✍ Scribed by Glenn H. Fredrickson, Kris T. Delaney

• Publisher: Oxford University Press
• Year: 2023
• Tongue: English
• Leaves: 399
• Series: International Series of Monographs on Physics, 173
• Category: Library

✦ Synopsis

This monograph provides an introduction to field-theoretic simulations in classical soft matter and Bose quantum fluids. The method represents a new class of molecular computer simulation in which continuous fields, rather than particle coordinates, are sampled and evolved. Field-theoretic simulations are capable of analysing the properties of systems that are challenging for traditional simulation techniques, including dense phases of high molecular weight polymers, self-assembling fluids, and quantum fluids at finite temperature.

The monograph details analytical methods for converting classical and quantum many-body problems to equilibrium field theory models with a molecular basis. Numerical methods are described that enable efficient, accurate, and scalable simulations of such models on modern computer hardware, including graphics processing units (GPUs). Extensions to non-equilibrium systems are discussed, along with an introduction to advanced field-theoretic simulation techniques including free energy estimation, alternative ensembles, coarse-graining, and variable cell methods.

✦ Table of Contents

cover
Titlepage
copyright
preface
Acknowledgements
contents
Introduction
Mathematical preliminaries
Functional notation
Functional calculus
Gaussian integrals
Delta functions and functionals
Phenomenological field theories
Molecularly-informed field theories
Auxiliary field representation
Coherent states representation
Continuous polymer chains
Bosonic quantum field theory
Classical Equilibrium Theory: Particles to Fields
Classical monatomic fluids
Density-explicit, auxiliary field representation
Auxiliary field representation
Auxiliary fields: potentials and smearing
Auxiliary fields: multiple components
Electrostatic interactions
Polymers and soft matter
Linear homopolymer melts and solutions
Coherent states representation
Continuous polymer chains
Other chain architectures
Multicomponent polymers and soft matter
Charged polymers
Quantum Equilibrium Theory: Particles to Fields
Particle representation and Feynman path integrals
Imposition of Bose symmetry
Path integral Monte Carlo
Coherent states field theory representation
Second quantization
Coherent states
Coherent states path integral
Field operators
Other ensembles and external potentials
Canonical ensemble
External potentials and artificial gauge fields
Quantum lattice models
Quantum spin models
Numerical Methods for Field Operations
Cells and boundary conditions
Pseudo-spectral methods
Periodic boundary conditions
Non-periodic boundary conditions
Modified diffusion equation
Higher spatial dimensions
Discrete chain models
Parallel computing and GPUs
Hardware trends
Software implementation
Numerical Methods for Field-Theoretic Simulations
Mean-field solutions
Root-finding versus optimization
Auxiliary field polymer models
Coherent state polymer models
Coherent state boson models
Including fluctuations: field-theoretic simulations
Models without a sign problem
Complex Langevin theory
Algorithms for AF polymer models
Algorithms for CS polymer models
Algorithms for CS boson models
Methodology, error analysis, and troubleshooting
Mean-field solutions
Field-theoretic simulations
Troubleshooting
Non-equilibrium Extensions
Quantum fluids and magnets
Non-equilibrium quantum field theory and Keldysh contours
Coherent states representation of the generating functional
Non-equilibrium field operators
Numerical methods
Classical polymers and soft matter
Phenomenological methods with a molecular basis
Hybrid methods: Single chain in a mean-field
Advanced Simulation Methods
Alternative ensembles
Isothermal–isobaric ensemble for classical polymers
Gibbs ensemble for classical polymers
Microcanonical ensemble for Bose fluid
Variable cell shape methods
Isothermal–isotension ensemble
Cell relaxation at fixed concentration c
Free-energy evaluation
Direct method
Thermodynamic integration
Bennett's acceptance ratio method
Coarse-graining methods
Variational force-matching
Extensions and opportunities
Linking particle and field-based simulations
Polymer formulations
Multi-scale modeling with particles and fields
Aqueous poly(ethylene oxide) solutions
Appendix A Fourier Series and Transforms
Appendix B Pressure and Stress Operators
Appendix C Linear Forces and the RPA
Appendix D Complex Langevin Theory
References
Index