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Computational Physics

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ISBN-10: 0521575885

ISBN-13: 9780521575881

Edition: 1999

Authors: J. M. Thijssen

List price: $60.00
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Description:

This book describes computational methods used in theoretical physics with emphasis on condensed matter applications. Computational physics involves the use of computer calculations and simulations to solve physical problems. Following an overview of the wide variety of topics and algorithmic approaches studied in this book, the text explores quantum scattering with a spherically symmetric potential as a typical example of a computational physics problem. The next chapters concentrate on electronic structure calculations, presenting the Hartree-Fock and Density Functional formalisms, and band structure methods. Later chapters discuss molecular dynamics simulations and Monte Carlo methods in classical and quantum physics, with applications to condensed matter and particle field theories. Each chapter begins with an exposition of necessary fundamentals, describes the formation of a sample program and ends with problems addressing related analytical and numerical issues. Useful appendices on numerical methods and random number generators are included and the book contains extensive references.
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Book details

List price: $60.00
Copyright year: 1999
Publisher: Cambridge University Press
Publication date: 6/17/1999
Binding: Paperback
Pages: 560
Size: 7.00" wide x 10.00" long x 1.00" tall
Weight: 2.046
Language: English

Preface to the first edition
Preface to the second edition
Introduction
Physics and computational physics
Classical mechanics and statistical mechanics
Stochastic simulations
Electrodynamics and hydrodynamics
Quantum mechanics
Relations between quantum mechanics and classical statistical physics
Quantum molecular dynamics
Quantum field theory
About this book
Exercises
References
Quantum scattering with a spherically symmetric potential
Introduction
A program for calculating cross sections
Calculation of scattering cross sections
Exercises
References
The variational method for the Schrodinger equation
Variational calculus
Examples of variational calculations
Solution of the generalised eigenvalue problem
Perturbation theory and variational calculus
Exercises
References
The Hartree-Fock method
Introduction
The Born-Oppenheimer approximation and the independent-particle method
The helium atom
Many-electron systems and the Slater determinant
Self-consistency and exchange: Hartree-Fock theory
Basis functions
The structure of a Hartree-Fock computer program
Integrals involving Gaussian functions
Applications and results
Improving upon the Hartree-Fock approximation
Exercises
References
Density functional theory
Introduction
The local density approximation
Exchange and correlation: a closer look
Beyond DFT: one-and two-particle excitations
A density functional program for the helium atom
Applications and results
Exercises
References
Solving the Schrodinger equation in periodic solids
Introduction: definitions
Band structures and Bloch's theorem
Approximations
Band structure methods and basis functions
Augmented plane wave methods
The linearised APW (LAPW) method
The pseudopotential method
Extracting information from band structures
Some additional remarks
Other band methods
Exercises
References
Classical equilibrium statistical mechanics
Basic theory
Examples of statistical models; phase transitions
Phase transitions
Determination of averages in simulations
Exercises
References
Molecular dynamics simulations
Introduction
Molecular dynamics at constant energy
A molecular dynamics simulation program for argon
Integration methods: symplectic integrators
Molecular dynamics methods for different ensembles
Molecular systems
Long-range interactions
Langevin dynamics simulation
Dynamical quantities: nonequilibrium molecular dynamics
Exercises
References
Quantum molecular dynamics
Introduction
The molecular dynamics method
An example: quantum molecular dynamics for the hydrogen molecule
Orthonormalisation; conjugate gradient and RM-DIIS techniques
Implementation of the Car-Parrinello technique for pseudopotential DFT
Exercises
References
The Monte Carlo method
Introduction
Monte Carlo integration
Importance sampling through Markov chains
Other ensembles
Estimation of free energy and chemical potential
Further application and Monte Carlo methods
The temperature of a finite system
Exercises
References
Transfer matrix and diagonalisation of spin chains
Introduction
The one-dimensional Ising model and the transfer matrix
Two-dimensional spin models
More complicated models
'Exact' diagonalisation of quantum chains
Quantum renormalisation in real space
The density matrix renormalisation group method
Exercises
References
Quantum Monte Carlo methods
Introduction
The variational Monte Carlo method
Diffusion Monte Carlo
Path-integral Monte Carlo
Quantum Monte Carlo on a lattice
The Monte Carlo transfer matrix method
Exercises
References
The finite element method for partial differential equations
Introduction
The Poisson equation
Linear elasticity
Error estimators
Local refinement
Dynamical finite element method
Concurrent coupling of length scales: FEM and MD
Exercises
References
The lattice Boltzmann method for fluid dynamics
Introduction
Derivation of the Navier-Stokes equations
The lattice Boltzmann model
Additional remarks
Derivation of the Navier-Stokes equation from the lattice Boltzmann model
Exercises
References
Computational methods for lattice field theories
Introduction
Quantum field theory
Interacting fields and renormalisation
Algorithms for lattice field theories
Reducing critical slowing down
Comparison of algorithms for scalar field theory
Gauge field theories
Exercises
References
High performance computing and parallelism
Introduction
Pipelining
Parallelism
Parallel algorithms for molecular dynamics
References
Numerical methods
About numerical methods
Iterative procedures for special functions
Finding the root of a function
Finding the optimum of a function
Discretisation
Numerical quadratures
Differential equations
Linear algebra problems
The fast Fourier transform
Exercises
References
Random number generators
Random numbers and pseudo-random numbers
Random number generators and properties of pseudo-random numbers
Nonuniform random number generators
Exercises
References
Index