Index 699Nos ́e–Hoover chain equations, 193
Nos ́e–Hoover equations, 190
Phase space function, 21, 70, 80, 108, 154,
501–504
work, 326
Phase space metric, 186–188
blue moon ensemble, 341
isokinetic equations, 204
Martyna–Tobias–Klein equations
flexible cell, 243
isotropic, 242
Nos ́e–Hoover chain equations, 194
Nos ́e–Hoover equations, 190
Phase transition, 169, 609
first order, 610
second order, 611
Planar Couette flow, 505, 520, 522, 524, 529
Planck’s constant, 365
Poincar ́e section, 9
Poisson bracket
classical limit of commutator, 379
conservation law, 22
definition, 22
Liouville operator, 108
Position Verlet, 132
Potential energy function
conservative forces, 10
Hard-sphere, 173
Lennard–Jones, 126
simple force field, 115
soft-sphere, 526
Potential of mean force, 325
Power spectrum, 570
Projection operator, 599
Propagator
classical, 109
adiabatic dynamics, 350, 352
constant-pressure molecular dynamics,
249
Mori–Zwanzig theory, 599–604
multiple time-scale integration, 117–254
Nos ́e–Hoover chain, 198
Suzuki–Yoshida factorization, 200
symplectic quaternion, 120
Trotter theorem, 110–115
unperturbed, 500
quantum, 374, 450
free particle, 457
imaginary time, 450
interaction picture, 536
path integral representation, 454, 463
relation to canonical density matrix, 450
time-dependent perturbation theory,
536–541
Wick rotation, 451
Quantum
amplitude, 366
expectation value, 366, 372
interference, 446
mechanics, 366
operator, 369
path integral, 366, 447
Pauli exclusion principle, 389, 415, 420,
427, 434
probability, 366
state vector, 368
wave equation, 377
wave function, 377
Quantum-classical correspondence principle,
377
Quaternions, 45–47, 119–121Radial distribution function
calculation of, 207–208
coordination number, 158
definition, 157
hard-sphere model, 173
isothermal-isobaric, 264
Lennard-Jones liquid, 157, 255
low-density limit, 211
perturbation theory, 173
relation to energy, 164
relation to pressure, 167
structure factor, 161
virial coefficients, 168
water, 158
Random force, 578–580
autocorrelation, 603
autocorrelation function, 579
Gaussian, 580
Random variable
Gaussian, 102–103
uniform, 285
Rare event, 306, 333–334, 336
RATTLE algorithm, 107–108, 256–261
Renormalization group, 634
block spin transformation, 635–636
decimation transformation, 647
fixed point, 637, 639–643
stable, 640, 642, 646
unstable, 640, 642, 643, 645
irrelevant variable, 644
linearized, 643–644
marginal variable, 644
pair cell transformation, 648
relevant variable, 644
universality, 645–646
Renormalization group equations, 636
Renormalization group flow, 640
Renormalized frequency, 586, 603
Replica exchange Monte Carlo, 300–304
Resonance instabilities in RESPA, 133
Rigid body, 37
equations of motion, 45
ROLL algorithm, 256–261
Rotation formula, 38
Rough energy landscape, 300, 333Sackur–Tetrode equation, 93, 275