Index 619
gluons, 528 , 529 , 532
strong interactions, 527 , 528
quantum electrodynamics (QED), 9 , 467 ,
512 – 514 , 517 , 518 , 527 – 531
quantum field theory, 9 , 15 , 342 , 466 , 467 , 469 ,
528
free field theory, 470 , 471 , 473 , 477 , 481 ,
482 , 512 , 533 , 535
gauge field theory, 528
non-abelian, 527
Wilson loop correlation function, 516 – 518 ,
520 , 530 , 535 , 536
Lehmann–Symanzik–Zimmermann relation,
472
regularisation, 474 , 530
renormalisable field theory, 475
scalar quantum field theory, 510
vacuum polarisation, 517 , 530
quantum molecular dynamics (QMD), 263 , 288
Car–Parrinello method, 267 , 272 , 278 , 284 ,
290
conjugate gradients method, 284 , 291 , 586
Hellmann–Feynman theorem, 98 , 266
primitive approximation, 407
quantum Monte Carlo (QMC), 8 , 96 , 100 , 114 ,
117 , 348 , 372 , 373 , 378 , 387 , 394 , 488 ,
540
checkerboard decomposition, 412
diffusion Monte Carlo (DMC), 391 , 395 , 402
fermion problem, 394
fixed-node method, 394 , 395
normal mode sampling, 409
path-integral Monte Carlo, 372 , 398 , 402 ,
406 , 407
primitive approximation, 406
transient estimator method, 397 , 414
variational Monte Carlo(VMC), 373 , 387 ,
389 , 391 , 394 , 420
virial expression for the energy, 417
local energy, 271 , 375 , 377 , 391 , 393 , 420
quantum scattering, 14
Born approximation, 27
differential cross section, 15 , 17 , 18 , 25 , 26
hydrogen/krypton, 17 , 18 , 23 , 24 , 27 , 177
phase shift, 16
scattering cross section, 16 , 17 , 22 , 25 , 110 ,
194 , 472
total cross section, 15 , 22 – 24 , 26
quasi Monte Carlo,seeMonte Carlo (MC), 299
Random number generators, 605 , 606
Gaussian distribution, 208 , 243 , 245 , 259 ,
385 , 409 , 480 , 481 , 490 , 519 , 609
Box–Müller method, 611
linear congruent, 606
Schrage’s method, 607 , 611
modulo random number generator, 611
nonuniform random numbers, 609
shift register random generator, 609
random numbers, 4 , 7 , 201 , 208 , 295 , 296 , 480 ,
490 , 605 – 609
truly random number, 299
random phase approximation (RPA), 106
real-space methods,see
band structure calculations, 288
reciprocal lattice,seecrystal lattices, 124
recurrence time, 200
recursion method, 22 , 76 , 288 , 334 , 495 , 558 ,
559 , 570 , 571 , 598 , 601 , 602
regula falsi method, 559
regularisation,seequantum field theory, 474
renormalisability,seequantum field theory, 475
renormalisation theory, 188 , 467 , 475 , 479 , 521 ,
530 , 531
residual minimisation by direct inversion of the
iterative subspace (RMDIIS) method,
286 , 588
restricted Hartree–Fock,seeHartree–Fock, 62
rigid molecules,seemolecular dynamics (MD),
234
Romberg method, 569 , 579
root-finding methods, 559
Roothaan equations,seeHartree-Fock, 69
routing, 547
Runge–Kutta integration method, 215
Runge–Kutta–Nystrom integrators, 215scalability, 556
scaling laws,seephase transition, 189
scattering cross section,seequantum scattering,
16
scattering resonance,seequantum scattering, 23
secant method, 111 , 559 , 560 , 603
self-avoiding walk (SAW), 320
self-consistency, 43 , 47 , 55 , 60 , 71 , 91 , 114 ,
122 , 156 , 157 , 163 , 273 , 284 , 584
self-consistent field (SCF) theory, 55
self-energy, 56 , 118 , 160 , 244
self-energy correction,seedensity functional
theory (DFT), 118
semi-empirical methods,seeelectronic structure
calculations, 130
SHAKE,seemolecular dynamics (MD), 240
shared memory, 546 , 549
shear viscosity, 252
Sherman–Morrison formula, 582
shift register random generator,seerandom
number generators, 608