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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 | |