Computational Physics

616 Index

Goedecker–Teter–Hutter (GTH)
pseudopotential, 154
gradient corrections,seedensity functional
theory (DFT), 96
grand canonical ensemble,seeensemble theory,
174
grand canonical potential, 174
graphene, 126 , 130 – 133
Grassmann anticommuting numbers, 513
gravitational interactions, 2
Green’s function, 107 , 108 , 138 , 161 , 167 ,
381 – 389 , 405 , 472 – 474 , 479

hard sphere liquid, 180 , 208 , 254 , 309
harmonic oscillator, 2 , 20 , 29 , 213 – 215 , 223 ,
253 , 264 , 375 , 376 , 378 , 387 , 389 , 393 ,
406 , 470 , 508 , 533 , 574
Hartree potential, 49 , 56 , 109 – 111 , 113 , 114 ,
157 , 163
Hartree-Fock
Coulomb operator, 58
exchange operator, 53
Fock operator, 54 , 55 , 59 , 62 , 63 , 83
Restricted Hartree-Fock(RHF), 62 , 64 , 85
Roothaan equations, 63 , 69 , 72
two-electron integral, 69 , 71 , 76 , 101
unrestricted Hartree–Fock (UHF), 62
Hartree–Fock theory, 43 , 49 , 56 , 78 , 90 , 91 , 101 ,
117 , 279
heat-bath algorithm,seeMonte Carlo (MC), 303
Heisenberg model, 350 , 410 , 411 , 413
helicity modulus,seeXYmodel, 502
helium atom, 46 , 109 , 121
Hellmann–Feynman theorem,seequantum
molecular dynamics (QMD), 98
Hessian matrix, 563 , 564
high performance computing, 540
highest occupied molecular orbital (HOMO),
103
Hohenberg–Kohn theorem, 108
Hoshen–Kopelman method, 464 , 495
host processor, 555
Householder method, 596 , 597
Hubbard model, 349 , 350 , 352 , 411
hybrid method, 485 , 510 , 525 , 527
hybrid Monte Carlo method, 489
hydrogen atom,seeelectonic structure, 110
hysteresis, 186 , 210

importance sampling,seeMonte Carlo (MC),
298
independent-particle approximation(IP), 46
infinitely deep potential well,seevariational
calculus, 290

initial value problem, 583 – 585

integrated correlation time,seecorrelation time,

193

integration algorithms

drift, 206 , 211 , 212 , 214 , 215 , 285

noise, 211 , 215 , 396 , 397 , 519 , 525 , 599

intermolecular interactions,seemolecular

dynamics (MD), 232

intramolecular interactions,seemolecular

dynamics(MD), 265

ionisation energy,83, 101– 104

ionisation potential, 78 , 101

irreducibility, connectedness, 300

Ising model, 10 , 180 – 182 , 185 – 190 , 304 ,

306 – 308 , 310 , 334 , 339 , 341 – 343 , 346 ,

347 , 366 , 367 , 415 – 417 , 466 , 476 , 491 ,

492 , 496 , 497 , 499 , 500 , 502

Jacobi method, 584 – 586

damped, 585

Janak’s theorem, 102 , 119

kinetic integral,seeHartree-Fock, 74

Klein–Gordon equation, 469

Kohn–Sham equations,seedensity functional

theory (DFT), 102

Kondo effect, 355

Korringa–Kohn–Rostocker (KKR) method,see

band structure calculations, 163

Kosterlitz–Thouless (KT) transition,seephase

transition, 500

Lagrange function, 292

Lagrange multiplier theorem, 58

Lagrangian, 225 , 229 , 234 , 237 , 238 , 269 , 290 ,

293 , 399 , 400 , 402 , 467 , 471 – 474 ,

511 – 513 , 516 , 521 , 522 , 533 , 534

Lanczos diagonalisation method, 417

Langevin dynamics, 247 , 251

Langevin equation, 249 , 250 , 257 , 382 , 385 ,

386 , 524 , 525

lattice Boltzmann method, 455 , 459

d2q6 grid, 456

d2q9 grid, 456

stick boundary conditions, 458

lattice field theory, 180 , 296 , 476 , 477 , 522 , 547

dynamical fermions, 521 , 522 , 524

lattice gas cellular automaton, 455

lattice spin systems, 10 , 398

lattice with a basis,seecrystal lattices, 123

leap-frog algorithm, 209 , 236 , 256 , 257 ,

487 – 490 , 554 , 574