698 Index
spin operators, 387–388
time evolution, 374, 540
time-ordering, 539
transfer matrix, 624–630
unitary, 374
Operator factorization
adiabatic dynamics, 350–351
Baker–Campbell–Hausdorff, 122
multiple time scale, 117, 201
Suzuki–Yoshida, 199
Trotter, 111
Orbital angular momentum, 14
Order parameter, 610, 617
Outer product, 370
Pair correlation function, 156
Pair-Wise additive
forces, 166
potential, 163, 166, 173, 211
Pairwise additive
forces, 4
potential, 293, 526
spin-spin interaction, 613
Parallel tempering, 301–303
Parity invariance
Ising model, 617
Particle reservoir, 268
Partition function
blue moon ensemble, 341
canonical ensemble
Wang–Landau algorithm, 304
classical canonical, 140
bead-spring model, 149, 150
configurational, 154
free particle, 144
harmonic bath, 147
harmonic oscillator, 147
ideal gas, 146
λ-dynamics, 318
relation to microcanonical partition
function, 140
separable Hamiltonian, 212
van der Waals theory, 175
classical grand canonical, 272, 273
ideal gas, 274
classical isoenthalpic-isobaric, 221
classical isokinetic, 202–205
classical isothermal-isobaric, 224, 231
ideal gas, 228
relation to canonical partition function,
225
classical microcanonical, 79
Andersen Hamiltonian, 239
harmonic bath, 95
harmonic oscillator, 95
ideal gas, 90
Nos ́e Hamiltonian, 181–182
thermal contact, 85
thermal reservoir, 138
classical non-Hamiltonian, 189
Nos ́e–Hoover algorithm, 190–191
constrained system, 213
definition, 70
Ising model, 619
mean-field, 619
one-dimensional, 624
two-dimensional, 626
quantum canonical, 401
discrete path integral representation, 476
harmonic oscillator, 404
identical particles, 471–475
path integral representation, 455, 459,
467
staging path integral representation, 478
quantum grand-canonical
ideal boson gas, 416
ideal fermion gas, 416
second quantization, 416
uniform ensemble, 83
Path integral
Born-Oppenheimer approximation, 494
classical isomorphism, 476
discrete, 454
functional integral, 462–471
influence functional, 493
path centroid, 481
Pauli exclusion principle, 389, 415, 420, 427,
434
Phase diagram, 610
Phase space, 6
accessible, 8
canonical distribution, 139
coarse-grained, 74, 79
distribution function, 67
driven harmonic oscillator, 496
ensemble average, 70
extended, 179–185
Nos ́e Hamiltonian, 180–183
Nos ́e–Hoover chain equations, 192–197
Nos ́e–Hoover equations, 185
Nos ́e–Poincar ́e Hamiltonian, 183–184
free particle, 6
grand canonical distribution, 271
harmonic oscillator, 7, 496
hill potential, 8
incompressibility, 23
isoenthalpic-isobaric distribution, 221
isothermal-isobaric distribution, 224
λ-dynamics, 322
nonequilibrium distribution, 500
Nos ́e–Hoover harmonic oscillator, 191
path-integral molecular dynamics, 480
projection operators, 599
shadow Hamiltonian, 122
steady state distribution, 497
trajectory, 6, 21
vector, 6, 48, 78, 198, 327, 351, 501
volume, 49, 66, 67, 187, 197
Phase space compressibility, 66, 186
isokinetic equations, 204