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