| Preface to the first edition | p. xi |
| Preface to the second edition | p. xiv |
| Introduction | p. 1 |
| Physics and computational physics | p. 1 |
| Classical mechanics and statistical mechanics | p. 1 |
| Stochastic simulations | p. 4 |
| Electrodynamics and hydrodynamics | p. 5 |
| Quantum mechanics | p. 6 |
| Relations between quantum mechanics and classical statistical physics | p. 7 |
| Quantum molecular dynamics | p. 8 |
| Quantum field theory | p. 9 |
| About this book | p. 9 |
| Exercises | p. 11 |
| References | p. 13 |
| Quantum scattering with a spherically symmetric potential | p. 14 |
| Introduction | p. 14 |
| A program for calculating cross sections | p. 18 |
| Calculation of scattering cross sections | p. 25 |
| Exercises | p. 27 |
| References | p. 28 |
| The variational method for the Schrodinger equation | p. 29 |
| Variational calculus | p. 29 |
| Examples of variational calculations | p. 32 |
| Solution of the generalised eigenvalue problem | p. 36 |
| Perturbation theory and variational calculus | p. 37 |
| Exercises | p. 39 |
| References | p. 41 |
| The Hartree-Fock method | p. 43 |
| Introduction | p. 43 |
| The Born-Oppenheimer approximation and the independent-particle method | p. 44 |
| The helium atom | p. 46 |
| Many-electron systems and the Slater determinant | p. 52 |
| Self-consistency and exchange: Hartree-Fock theory | p. 54 |
| Basis functions | p. 60 |
| The structure of a Hartree-Fock computer program | p. 69 |
| Integrals involving Gaussian functions | p. 73 |
| Applications and results | p. 77 |
| Improving upon the Hartree-Fock approximation | p. 78 |
| Exercises | p. 80 |
| References | p. 87 |
| Density functional theory | p. 89 |
| Introduction | p. 89 |
| The local density approximation | p. 95 |
| Exchange and correlation: a closer look | p. 97 |
| Beyond DFT: one-and two-particle excitations | p. 101 |
| A density functional program for the helium atom | p. 109 |
| Applications and results | p. 114 |
| Exercises | p. 116 |
| References | p. 119 |
| Solving the Schrodinger equation in periodic solids | p. 122 |
| Introduction: definitions | p. 123 |
| Band structures and Bloch's theorem | p. 124 |
| Approximations | p. 126 |
| Band structure methods and basis functions | p. 133 |
| Augmented plane wave methods | p. 135 |
| The linearised APW (LAPW) method | p. 141 |
| The pseudopotential method | p. 144 |
| Extracting information from band structures | p. 160 |
| Some additional remarks | p. 162 |
| Other band methods | p. 163 |
| Exercises | p. 163 |
| References | p. 167 |
| Classical equilibrium statistical mechanics | p. 169 |
| Basic theory | p. 169 |
| Examples of statistical models; phase transitions | p. 176 |
| Phase transitions | p. 184 |
| Determination of averages in simulations | p. 192 |
| Exercises | p. 194 |
| References | p. 195 |
| Molecular dynamics simulations | p. 197 |
| Introduction | p. 197 |
| Molecular dynamics at constant energy | p. 200 |
| A molecular dynamics simulation program for argon | p. 208 |
| Integration methods: symplectic integrators | p. 211 |
| Molecular dynamics methods for different ensembles | p. 223 |
| Molecular systems | p. 232 |
| Long-range interactions | p. 241 |
| Langevin dynamics simulation | p. 247 |
| Dynamical quantities: nonequilibrium molecular dynamics | p. 251 |
| Exercises | p. 253 |
| References | p. 259 |
| Quantum molecular dynamics | p. 263 |
| Introduction | p. 263 |
| The molecular dynamics method | p. 266 |
| An example: quantum molecular dynamics for the hydrogen molecule | p. 272 |
| Orthonormalisation; conjugate gradient and RM-DIIS techniques | p. 278 |
| Implementation of the Car-Parrinello technique for pseudopotential DFT | p. 289 |
| Exercises | p. 290 |
| References | p. 293 |
| The Monte Carlo method | p. 295 |
| Introduction | p. 295 |
| Monte Carlo integration | p. 296 |
| Importance sampling through Markov chains | p. 299 |
| Other ensembles | p. 310 |
| Estimation of free energy and chemical potential | p. 316 |
| Further application and Monte Carlo methods | p. 319 |
| The temperature of a finite system | p. 330 |
| Exercises | p. 334 |
| References | p. 335 |
| Transfer matrix and diagonalisation of spin chains | p. 338 |
| Introduction | p. 338 |
| The one-dimensional Ising model and the transfer matrix | p. 339 |
| Two-dimensional spin models | p. 343 |
| More complicated models | p. 347 |
| 'Exact' diagonalisation of quantum chains | p. 349 |
| Quantum renormalisation in real space | p. 355 |
| The density matrix renormalisation group method | p. 358 |
| Exercises | p. 365 |
| References | p. 370 |
| Quantum Monte Carlo methods | p. 372 |
| Introduction | p. 372 |
| The variational Monte Carlo method | p. 373 |
| Diffusion Monte Carlo | p. 387 |
| Path-integral Monte Carlo | p. 398 |
| Quantum Monte Carlo on a lattice | p. 410 |
| The Monte Carlo transfer matrix method | p. 414 |
| Exercises | p. 417 |
| References | p. 421 |
| The finite element method for partial differential equations | p. 423 |
| Introduction | p. 423 |
| The Poisson equation | p. 424 |
| Linear elasticity | p. 429 |
| Error estimators | p. 434 |
| Local refinement | p. 436 |
| Dynamical finite element method | p. 439 |
| Concurrent coupling of length scales: FEM and MD | p. 440 |
| Exercises | p. 445 |
| References | p. 446 |
| The lattice Boltzmann method for fluid dynamics | p. 448 |
| Introduction | p. 448 |
| Derivation of the Navier-Stokes equations | p. 449 |
| The lattice Boltzmann model | p. 455 |
| Additional remarks | p. 458 |
| Derivation of the Navier-Stokes equation from the lattice Boltzmann model | p. 460 |
| Exercises | p. 463 |
| References | p. 454 |
| Computational methods for lattice field theories | p. 466 |
| Introduction | p. 466 |
| Quantum field theory | p. 467 |
| Interacting fields and renormalisation | p. 473 |
| Algorithms for lattice field theories | p. 477 |
| Reducing critical slowing down | p. 491 |
| Comparison of algorithms for scalar field theory | p. 509 |
| Gauge field theories | p. 510 |
| Exercises | p. 532 |
| References | p. 536 |
| High performance computing and parallelism | p. 540 |
| Introduction | p. 540 |
| Pipelining | p. 541 |
| Parallelism | p. 545 |
| Parallel algorithms for molecular dynamics | p. 552 |
| References | p. 556 |
| Numerical methods | p. 557 |
| About numerical methods | p. 557 |
| Iterative procedures for special functions | p. 558 |
| Finding the root of a function | p. 559 |
| Finding the optimum of a function | p. 560 |
| Discretisation | p. 565 |
| Numerical quadratures | p. 566 |
| Differential equations | p. 568 |
| Linear algebra problems | p. 590 |
| The fast Fourier transform | p. 598 |
| Exercises | p. 601 |
| References | p. 603 |
| Random number generators | p. 605 |
| Random numbers and pseudo-random numbers | p. 605 |
| Random number generators and properties of pseudo-random numbers | p. 606 |
| Nonuniform random number generators | p. 609 |
| Exercises | p. 611 |
| References | p. 612 |
| Index | p. 613 |
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