Computational Physics

Index 615

energy estimator, 213 , 214 , 256 , 396 , 397 , 406
energy functional, 267 , 268 , 290 – 293 ; see also
variational calculus, 39
energy surface, 212 , 487
energy-independent pseudo potentials,seeband
structure calculations
ensemble average,seeensemble theory, 313 ,
316
ensemble theory, 170 , 311
canonical (NVT) ensemble, 172 , 299 , 311 ,
313 , 314 , 316
ensemble average, 171 , 172 , 174 , 175 , 178 ,
179 , 183 , 192 , 193 , 197 , 229 , 230 , 302 ,
311 , 316 – 318
grand canonical ensemble, 174 , 310 , 312 , 313
microcanonical (NVE) ensemble, 200 , 207
partition function, 7 , 8 , 172 – 174 , 177 , 180 ,
185 , 190 , 228 , 229 , 231 , 311 , 317 , 318 ,
325 , 326 , 339 , 340 , 398 – 400 , 402 , 403 ,
406 , 478 , 485 , 515 – 517 , 526 , 537
equation of state, 3 , 207 , 312
ergodicity, 183
Euler equations,seefluid dynamics, 236 , 423
Euler’s forward method, 571
Ewald method, 243 , 245
Ewald–Kornfeld method, 244
exchange correlation,seedensity functional
theory (DFT), 90
exchange correlation hole, 99 , 100
exchange hole, 54 , 91 , 100 , 113
exponential correlation time,seecorrelation
time

F model, 370
face centred cubic,seecrystal lattices, 123 , 309
false position (regula falsi) method, 559
farmer–worker paradigm, 551
fast Fourier Transform (FFT), 153 , 288 , 481 ,
509 , 587 , 599 – 601
Danielson–Lanczos lemma, 601
fast multipole method (FMM), 247
fermion problem,seequantum Monte Carlo
(QMC), 390
Feynman, 372 , 398
FFTW package, 153
finite difference grid, 584 , 594
finite difference method, 5 , 448 , 579 , 581
finite difference method 31 , 578
finite element method, (FEM), 5 , 423 , 424 , 448 ,
444
adaptive refinement, 424 , 434 , 439
local error estimator, 434
local refinement, 439
finite-size scaling,seephase transition, 476

fixed-node method,seequantum Monte Carlo

(QMC), 394

floating point operation (FLOP), 542

fluctuation-dissipation theorem, 250 , 252

fluid dynamics, 448

binary system, 449 , 459 , 464

Euler equations, 451

Navier–Stokes equations for fluid dynamics,

448 , 449 , 460 , 463

Flynn’s classification, 545

multiple instruction multiple data stream

(MIMD), 545 , 546 , 553

multiple instruction single data stream

(MISD), 545 , 546

single instruction multiple data stream

(SIMD), 545 , 546 , 549

single instruction single data stream (SISD),

545 , 546 , 550

Fock matrix, 64 , 70–72, 87 , 271 , 273 , 274 , 276 ,

279

Fock operator,seeHartree–Fock, 80

Fokker–Planck equation, 250 , 384 – 386 , 391 ,

490

force fields, 258 , 263 , 265

Fourier-accelerated Langevin method, 507 – 510

fractal dimension, 11 – 13

free energy calculation, 176 , 316

free field theory,seequantum field theory, 470

Frobenius’ theorem, 342

front-end computer, 555

fundamental postulate of statistical mechanics,

170

gauge field theory,seequantum field theory, 516

Gauss–Legendre integration, 176

Gauss–Seidel method, 423 , 481 , 585 , 587

Gaussian distribution,seerandom number

generators, 473

Gaussian product theorem, 73 , 74

Gaussian type orbitals (GTO),seebasis sets,

272

Gear algorithms, 215

Gell–Mann matrices, 529

generalised eigenvalue problem,seeeigenvalue

problem, 32

generalised gradient approximation, 101

generalised Metropolis method,seeMonte

Carlo (MC), 303

genetic algorithm, 329

Gibbs ensemble method,seeMonte Carlo

(MC), 314

Gibbs–Duhem relation, 174

gluons,seequantum chromodynamics (QCD)

and quarks, 528