Das Sh.P. Statistical Physics of Liquids at Freezing and Beyond
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Index
-derivable theory, 512
φ
4
model, 514
activated process, 122, 182
activation energy, 165, 171, 425
Adam–Gibbs theory, 487
adiabatic approximation, 294, 345, 379, 416
adsorption, 90
aging, 169, 184, 449, 450, 460, 471, 473, 477,
481, 482
amorphous solid, 164, 170, 250, 251, 256, 257, 301, 303, 388,
429, 447, 459, 490, 498, 530, 536
amorphous structure, 169, 182, 494, 498, 536
angle
azimuthal, 151
polar, 151
anharmonic
crystal, 84
glass, 170
anti-ferromagnetic interaction, 190
aperiodic structure, 188,
491, 492, 494, 495
argon (Ar), 46
Arrhenius relaxation, 165
autocorrelation function
concentration, 217
density, 39, 40, 169, 200, 215, 216, 244, 331, 345, 366,
414, 427
equilibrium averaged, 37
longitudinal current, 40
noise, 273, 361
tagged-particle velocity, 46
transverse current, 240
Bain’s distortion, 148
balance equations, 205
ballistic regime, 193
barrier
effective potential, 503
free energy, 117, 118, 120, 121, 127, 128, 130, 134, 150,
152–154, 161, 411, 425, 494
hopping, 410, 489
potential energy, 27, 182, 186, 414
, 489, 490, 496
barrier hopping, 182
basic vectors for cluster symmetry, 156
basin
energy, 183
free energy, 184
free-energy landscape (FEL), 191, 448, 498, 505,
506, 510
hopping, 186
of attraction, 448
potential-energy landscape (PEL), 183, 186
vibrational motion, 187
BBGKY hierarchy, 24
Bennett’s algorithm, 492
binary
collision, 10, 44, 170, 222, 243, 272, 427
mixture, 184, 193, 212, 214, 295, 296, 298, 299,
379, 383
soft-sphere mixture, 407, 497, 527
blip function, 33
Boltzmann
collision term, 223
collision time
t
a
, 44
constant
k
B
, 3
equation, 10, 222, 224
factor, 92, 230
H-theorem, 10
transport coefficients
shear self-diffusion coefficient, 223
shear viscosity, 223
thermal conductivity, 223
bond, 497
bond breaking, 497
bond-orientational order parameter, 155, 497
boson peak, 259
bridge function, 31
Brillouin peaks, 241
broken symmetry, 247
Brownian motion, 50, 56, 225, 304, 394, 416
558
Index 559
cage, 171, 174, 193, 220, 371, 409, 414,
455, 529
capillary waves, 101
cell picture, 174
chemical potential
at coexistence, 69
at interface, 118
binary mixture, 214
critical nucleus, 127
hard-sphere system, 153
ideal gas, 15
local equilibrium, 208
solid phase, 80
CKN, 403
Clapeyron equation, 6, 71
close-packed f.c.c. structure, 59
cluster, 181
coarse-graining length scale
density function, 85
hydrodynamics, 243
collective density, 225
collision integral, 11
collisionless approximation, 10
colloids, 153, 293, 303, 395, 406
complexity, 487
compressibility
equation, 22, 30, 75
isothermal, 18
compressible liquid
1/ρ nonlinearity, 292
concentration, 122
concentration equation, 214
concentration variable, 212, 221, 296
condensation, 117
conditional probability, 20
conductivity
electrical, 164
thermal, 210, 224, 268
conjugate fields, 457
conservation
energy, 207
mass, 207
momentum, 207, 341, 408
probability, 41, 396
tagged-particle density, 376
conservation laws, 205
conservation of angular momentum, 262
continued fraction, 216, 240, 380, 382
continuity equation, 7, 38, 209, 221, 235, 246, 267, 377
cooling rate, 165
cooperative effects, 44
cooperatively rearranging regions (CRRs), 487
correction to scaling in MCT, 375, 376, 382, 402,
405, 410
Coulomb force, 10
critical
coupling, 464
decay, 402
density, 371
domain, 495
dynamic phenomena, 276
dynamics, 319, 337
exponent, 410
nucleus, 120, 131, 133–135, 138, 147, 495
phenomena, 104, 490
point, 201, 271
surface, 368
temperature, 402
CRN, 402
cusp in NEP, 373
damping, 215
damping matrix, 238, 321
de Broglie wavelength, 3, 15, 20, 65, 183, 298, 394,
436, 491
de Gennes narrowing, 245
Debye
density of states, 115
frequency, 115
integral, 115
model, 78
relaxation, 192
temperature, 115
Debye
T
3
law, 259
Debye model, 259
Debye–Waller factor, 372
defect density, 251
density expansion
direct correlation function, 75
transport coefficients, 224
density-functional theory (DFT), 58, 59, 68, 70, 79, 81, 91,
106, 115
elastic constant, 84
detailed balance, 189, 459
determinant, 258
deterministic, 8, 50, 215, 358, 395
dielectric, 164, 400, 402, 453, 473
diffraction peak, 245
diffusion coefficient
Brownian particle
¯
D
0
, 54
collective density
D
0
, 399
tagged particle, 128, 173
diffusion in disordered media, 319
diffusion in random media, 319
diffusion of vortices, 272
diffusive heat mode, 241
direct correlation function
from WDA, 75
higher-order, 66
560 Index
one-particle, 67
Ornstein–Zernike, 71
two-particle, 26
dispersion relations, 234
displacement vector
u, 250
domain growth problem, 319
double-well potential, 131
driven diffusive systems, 319
driven interfaces in random media, 319
dynamical heterogeneity, 192, 383
dynamics of liquid crystals, 319
effective
Debye–Waller factor, 402
diameter of binary mixture, 185
interactions , 406
liquid in MWDA, 74
potential, 494, 500
temperature, 451, 453, 471, 472, 527
eigenvector, 372, 534
Einstein
frequency, 44, 55, 455
relation for diffusion, 54, 159, 193, 220
summation convention, 227, 277
elastic
constant, 84, 253
displacement, 236
energy, 180
fourth-rank tensor, 302
scattering, 24
solid, 252, 255
strain tensor, 252, 301
stress tensor, 252
embryo, 155
ensemble
canonical, 20
equilibrium, 358
ergodic hypothesis, 6
grand-canonical, 60, 105
isobaric, 19
local equilibrium,
450
micro-canonical, 14
nonequilibrium, 207
thermodynamics, 19
trace, 12, 230
Enskog
collision time
t
E
, 44, 244, 383
tagged-particle dynamics, 380
transport coefficients
self-diffusion coefficient, 223
shear viscosity, 223
thermal conductivity, 223
Enskog theory, 174, 223, 245
modified, 224
enthalpy, 127, 155, 167, 211
entropic droplet, 495
entropy, 13, 81, 166, 209
configurational, 183, 488, 503, 506, 521
crisis, 494, 503, 519
drive, 495
production rate, 264
supercooled liquid, 486
thermodynamic, 529
vibrational, 505, 529
equation of state
Carnahan–Starling, 30, 72, 80
from compressibilty condition, 29
from virial condition, 29
ideal gas, 65, 125
Percus–Yevick, 72, 78, 102
equimolar mixture, 387
equipartition law, 237
Euler equations, 207, 263, 297
Euler–Lagrange equation,
137, 162
exchange interactions, 419
excluded volume, 379
facilitated spin models, 399
factorization property, 374
Feynman graphs, 326
Fick’s law, 211
fictive temperature, 451, 474
finite-size scaling, 202
fluctuating hydrodynamics, 205
binary mixture, 295
compressible liquid, 287
for crystal, 246
linear, 225, 238
nonlinear (NFH), 238, 271
fluctuation–dissipation relation
bare transport matrix, 238, 287
MSR theory, 291, 321, 335
tagged-particle dynamics, 378
fluctuation–dissipation theorem
p-spin model, 424
compressible liquid, 340
generalized, 443
Langevin equation, 232
linear-response theory, 49
MSR theory, 334, 435
violation, 443
flux-lattice melting, 90
Fokker–Planck equation, 189, 190, 283, 394, 395
Fokker–Planck operator, 394
four-point correlation functions, 195, 201, 362,
385, 426
four-point kernel, 325
four-point vertex functions, 344