1-s2 0-S1874562806800100-main

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Subject Index 
Absorption coefficient 148 
Absorption strength 184 
Ag + 142 
Ag + electronic quadrupolar deformability 
200 
Ag + electronic transitions in KI: Ag + 
optical transitions 174 
Aging 175 
Aging and reactivation of isolated Ag + 
defect centers in KI 176 
AlxGal_xAs 355, 356, 367, 369, 
370-372, 374, 377, 381-385, 
388, 394 
Alkali halides 141 
Analytical treatments 6 
Anharmonic effects 124 
Anharmonic perturbation theory 111-113, 
115 
Anharmonic ZBM frequency 228 
Anharmonicity 95, 109 
Anisotropic media 302 
Anisotropic solids 275 
Ar 97, 110, 112, 115, 119 
Associated Legendre function 298 
Asymptotic ILM behavior 210 
Atom host 264 
Atom substitutional 264 
distribution function 327 
impurities 326 
number of 328 
random variable 264, 327 
Backward-wave oscillators 170 
Ballistic phonons 282 
Beams of phonons 279 
Bethe ansatz 111 
Boltzmann equation 291,292, 295 
Chapman-Enskog approximation 302 
collision invariants 306 
collision operator 287 
-spectrally decomposed 287 
relaxation time approximation 283 
solution for cubic and elastic media 
306 
source term 282 
Boltzmann factor 107 
Boltzmann kinetic equation 271 
Boltzmann population 162 
Born-Mayer plus Coulomb (BMC) 
potential 237, 238 
Bosons 9 
Branches longitudinal 119 
Branches transverse 119 
Bravais lattices 269 
Brillouin zone 105, 108 
first 104 
Broadening of a spectral line 
inhomogeneous 281 
Bulk modulus 108 
Christoffel equation: plane waves solution 
274 
Classical mechanics 
time reversal invariance 335 
-violation by collisions 335 
Classical Monte Carlo methods (CMC) 
10-18, 111, 112, 115, 119 
Classical partition function 11 
Clausius-Mossotti equation 167 
Coherent potential approximation 373 
523 
524 Subject index 
Collision integral 273, 276, 277, 290 
collision invariant 290 
decomposed form 287 
general structure 
-continuous part 307 
-discrete part 307 
nonpositive 290 
spectral decomposition 290 
spectrum of relaxation rates 278 
Collision invariant 278, 302, 273 
Collision operator 302, 305, 310 
nonpositive 305 
spectrum 
-continuous 302 
-discrete 302 
-eigenvalues related to collision 
invariants 302 
Collision rates 305 
Collision term 272 
Collision theory 
detector 329 
differential cross-section 329 
incident beam 329 
incident flux 329 
target 329 
wave packets 329 
Complex dielectric constant 167 
Continued fraction 53-58, 63, 64, 69-71, 
122 
expansion 53 
representation 53, 120 
Continuum deformation field 273 
Coulomb potentials 106 
Crystalline lattice 
long-wavelength limit 273, 274 
energy transport in 270 
fluctuations in mass distribution 263 
-scattering on 263 
quasimomentum transport in 270 
spatially homogenous 269 
spatially inhomogeneous 268, 269, 
280 
structural defects 280 
with basis 269 
Crystals 
Lu3A15012 325 
of Ge, GaAs, InSb, Si 273 
solid solutions 325 
Cubic anharmonicity 147 
Cubic materials 307 
Cubic media 302 
Cumulant expansion 132 
Curie point 129 
Curie-Weiss law 128 
(6, 6', 6") model 199 
4d 1~ -+ 4d95s parity-forbidden eleet,-onic 
transitions 175 
DC lattice distortions 147 
Debye frequency 156 
Debye model 167 
Debye temperature 115, 279, 323, 325 
Debye-Waller factor 121, 158 
Decomposition of the fourth-rank unit 
tensor 303 
Density matrix 85, 132 
Detailed balance 14 
Diatomic chain 362 
Diffusion 
coefficient 292, 294 
equation 301 
flows 299 
matrix 307 
Dipole moment 183 
Dispersion curve 221 
Dispersion curves for moving ILMs 236 
Dispersive phonons 273 
Displacement patterns 187 
for different KI:Ag + modes 188 
Displacive model 126 
Displacive model ferroelectric 127, 129 
Distribution function 295, 296, 313 
Chapmann-Enskog expansion 299 
deviation from state of incomplete 
equilibrium 300 
Fourier harmonics 299 
Fourier transform 295, 300, 301 
-time dependent 295 
Fourier-Laplace transform 296, 300, 
313 
-set of poles 313, 317 
-singular continuum 312 
-singularities 300 
incomplete equilibrium state 301 
initial condition 295 
long-time diffusion asymptotics 295 
time reversed 271 
true thermodynamic equilibrium 302 
Double-well order-disorder model 126 
Subject index 525 
Effective potential 87, 89, 90, 92, 96-98, 
107, 108, 117, 126, 127, 131 
formalism 125 
formulation 67-71 
method 130 
Monte Carlo method (EPMC) 107, 
108, 110-112, 115-117, 121 
theory improved 132 
E-field dependence of the resonant mode 
160 
Elastic constants 306 
symmetry relations 274 
Voigt symmetry 274 
Elastic media 
anisotropic 273, 276 
basic fourth rank tensors 308 
Christoffel equation 273 
cubic 278, 295, 310 
-diffusion coefficient 307 
-elastic properties 306 
-scattering properties 306 
-transversely isotropic 295 
density 273 
hexagonal 278 
isotropic 278, 290, 301,310 
of arbitrary symmetry 311 
of lower symmetry 291 
tensor of elastic constants 273, 274 
tetragonal 278 
transversely isotropic 278, 307, 308 
-tensor of [[V2] 2] class 309 
trigonal 278 
Electric field 
measurements 152, 198 
Stark effect 143 
Electron gas: 2D electron gas 283 
Energy density current 283 
Entropy 272 
current density 272 
density 272 
local balance 272 
production 272 
Envelope solitons 146 
Equal time correlation functions 122 
Equilibrium statistical mechanics 121 
Euclidean space 273 
Even ILM stability 219 
Even moments 121 
Even parity ILM 213 
Even-symmetry resonant modes 179 
Exact ILM frequency 212 
Excitons: cloud of 283 
FCC Lennard-Jones crystal 16-18, 
44-52, 69-71 
Fermi golden rule 335 
Ferroelectric model 96 
Ferroelectrics 124, 128, 131, 144 
Filtering transformations 53 
First-order effective potential 116 
First-order self-consistent phonon 
approximation 67-69 
First-order transition 126 
Fluctuations 90, 93 
Focusing (enhancement) factor 286 
Force-constant matrix 111 
Four-fold axes of a cubic crystalline 
structure 302 
Fourth rank tensor decomposition 302 
Fourth-neighbor pocket isotope modes 
192 
Free energy 86, 87, 101, 106 
Free-end boundary condition case 236 
Free rotor states 172 
Frequency moments 53-64, 69-71 
f sum rule 152 
GaAs/AlxGal_xAs 418 
(GaAs)l_xGe2x 405, 406, 414, 415, 417 
GaAsl_xSbx 393, 394 
Gal_xlnxAs 385-388, 390 
Gal_zlnxSb 390, 392 
(GaSb)l_xGe2x 405, 406, 408-413, 
416--418 
Gap ILMs 238 
Gap modes 141 
Gas of phonons 279 
collisionless regime 299 
incomplete equilibrium state 299 
local equilibrium state 299 
rarefied 279 
Gaussian 126 
Gaussian approximation 57, 58, 63, 64 
Gaussian pair distribution 93 
Gaussian sampling 17 
Gaussian smearing 88 
Ginzburg expansion 111, 116, 119, 120 
Ginzburg parameters 96, 97, 116 
Gram-Schmidt procedure 54 
Green's function Monte Carlo method 6 
526 Subject index 
Green's harmonic function 182 
Ground state tunneling systems 168 
Group velocity 222, 270 
Grtineisen parameter 17 
Haldane conjecture 8 
Hamiltonian equations 335 
Harmonic oscillator 86, 89-91, 125, 132 
He 97 
Heat capacity 107, 108, 112, 115 
Heat conductivity coefficient 291, 310 
Heat pulse 
ballistic component 324 
diffusive component 324 
transmiss/ion experiments 279 
Heisenberg antiferromagnet 8 
Heisenberg spin systems 7 
Hubbard model 8, 43 
Hydrostatic pressure 154 
measurements 169 
Identical particles 42-44 
ILM (intrinsic localized mode) and static 
distortion 231 
ILM and zone boundary mode stability 
227 
ILM collisions 225 
with a mass defect 227 
ILM dynamic and static displacement 
pattern 231 
ILM in glass 249 
ILM induced force constant 
renormalization 233 
ILM instability growth rates 219 
ILM motion 235 
ILM power spectra 242 
ILM stability 215 
ILMs and diatomic lattices 239 
ILMs and (k2, k3, k4) potentials 228 
ILMs and realistic potentials 236 
ILMs even-parity 144 
ILMs stability 146 
ILMs traveling 146 
Improved numerical convergence 25-27, 
35-39, 46, 47 
Improved self-consistent phonon theory 
(ISC) 116, 117, 118 
Impurity modes 141 
Impurity-induced dielectric constant 167 
InAsl_xSbx 392, 393 
Inert gas 115 
Inert-gas crystals 97, 112 
Infinitesimal displacement 218 
Inl_xGaxAsuSbl_y 395,397 
Initial state, spatially homogeneous 305 
Internal energy 107, 108, 110, 114, 117 
Intrinsic localized modes (ILM) 143, 206, 
207 
IR-active "isotope" pocket gap modes 189 
Ising model 8 
Isotope effect 143 
Isotope mode intensity temperature 
dependence 195 
Isotope mode splitting 189 
Isotropic 
approximation 116, 117 
media 302 
tensor 278 
trial function 118 
KI 173 
KI alloys 173 
KI phonon gap 160 
KI + 1 mole% RbI + 0.2 mole% Ag + 
173 
KI:Ag + aging 175 
KI:Ag + (~, ~') model 185 
KI:Ag + Debye spectrum 167 
KI:Ag + impurity 142 
KI:Ag + pocket mode experiments 193 
39K+ __+ 41K + host-lattice isotopic 
substitution 191 
(k2, k4) lattice 209 
Knudsen number 292, 307 
Lattice 
constant 47-49 
disorder 173 
dynamics 104 
sound velocity 221 
spacing 116 
unit cell 340 
Lattice Hamiltonian 
anharmonic part 264, 265 
harmonic approximation 266 
harmonic part 265 
part containing isotope scattering 
264, 334 
Law of mass action 245 
Subject index 527 
Lennard-Jones 
chain 123 
interaction 122 
parameters 118 
potential 18, 93, 111, 115, 237, 238 
solid 18 
Lifshitz method 182 
Lifshitz theory 142 
Linear chain 90 
Linear coupling between a resonant mode 
and a Debye spectrum 159 
Liouville equation 270 
Liquid helium 9 
Local hydrodynamic parameters 270 
Local modes 141 
Long-wavelength acoustic phonons 265, 
269, 276-279 
Low coupling approximation (LCA) 98, 
99, 104, 105, 107, 108, 110, 
111, 119, 120 
Many fermion systems 9 
Markovian generation process 13 
Mass defect 225 
Mass difference scattering 273 
Material tensor 278 
fourth rank tensor algebra 288 
number of independent elements 278 
MD simulations 235 
Metropolis sampling 9, 10, 14-17 
Microreversibility 342 
Microreversibility principle 269 
Microwave absorption 170 
Microwave transition 170 
Molecular dynamics (MD) 123, 131, 144, 
210 
simulations 122 
Molecular field 124 
Molecular field ansatz 124 
Mollwo-Ivey rule 150 
Moment expansion 128, 131 
Moment expansion method 123 
Moments 121, 128 
Monte Carlo simulation 107-109, 115, 
131 
Morse potential 237, 238 
MOssbauer recoilless fraction 246 
Nearest neighbor distance 114 
Nearest-neighbor cubic anharmonicity 230 
Ne 97, 110, 115, 120 
22Ne 117 
Non-crystalline solids 353 
harmonic 353 
Non-identical particles 9 
Nonresonant absorption 160, 167 
Normal coordinates 101 
Normal modes 101 
Normal mode frequencies 106 
Number density of phonons 306 
Odd parity ILM 210 
Odd parity ILM gap mode 241 
in the diatomic lattice 241 
Odd- and even-ILM patterns 223 
Off-center configuration 142, 172 
Off-center population 169 
On-center configuration 142 
One-dimensional 
anharmonic potential 20 
chain 28--44, 52-64, 69, 70, 359 
lattice 110 
models 111 
system 124 
One-phonon approximation 121 
One-phonon spectral function 128 
Operator 
antilinear 337 
antiunitary 338, 339 
antiunitary conjugation 339 
complex conjugation 339 
Order parameter 125-127 
Order-disorder model ferroelectric 126, 
127, 129 
Oscillator strength temperature dependent 
signature 178 
Oversized nonresonant cavity technique 
170 
Paraelectric resonance 169 
Parallel computer: Connection Machine 
120 
Partition function 20-23, 26, 30, 31, 36, 
43, 44, 46, 66, 67, 85, 86, 89, 
106, 108, 109, 111, 120, 124, 
130, 131 
Path integral 85, 87 
Path integral theory 131 
Path integral methodology 7 
528 Subject index 
Path integral techniques 6 
Pauli equation 343 
Pauli master equation 268, 332 
Peierls inequality 87, 131 
Periodic boundary conditions 214 
Phase perturbations 218 
Phase transitions 131 
displacive 124 
of 1st order 125 
order-disorder 124 
Phonon 
acoustic dispersive 279 
acoustic: mean free path 293 
annihilation operator of 266 
ballistic: Monte Carlo computer 
experiment 286, 287 
ballistic motion 287 
ballistic beams 280 
collision integral 270, 289, 303 
collision operator 288, 291 
coupling with deformation field 271 
creation operator 266 
Debye velocity 277 
densities 285 
densities of energy 285 
densities of quasimomentum 285 
detector 281,282 
-fixed 281 
-movable 281 
-sensitive to energy 281,283 
-sensitive to quasimomentum 281, 
283 
diffusion coefficient 325 
diffusion equations 291,294 
diffusive motion 287 
dispersion law degeneration points 
268 
dispersion 279 
-distribution function 270, 287, 289, 
292 
-diffusive behaviour 319, 323 
-incomplete equilibrium state 289 
-of complete equilibrium 289 
distribution transient 280 
equilibrium system of phonons 345 
focusing 287 
focusing (imaging) experiments 284 
frequencies 132, 278 
gas entropy 272 
gradient of frequency 275 
Phonon 
group velocity 274-276, 281,288 
high energy acoustic 279 
injected Planckian 323 
isotope scattering 295, 311 
-contribution to heat conductivity 
coefficient 311 
local thermal equilibrium 323 
long-wavelength acoustic 271 
low energy acoustic 279 
mediated detectors of elementary 
particles 279 
number density 278, 287, 291 
number operator eigenvectors 266, 
267 
-normalization condition 267 
-orthogonality condition 267 
occupation number 345 
occupation number's Planck function 
345 
operator 341 
-annihilation of 340, 341 
-creation of 340, 341 
-number of 341 
-total number of 341 
optical 279 
phase velocity 274-276, 288 
plane waves representation 269 
polarization 
-conversion processes 302 
-quasilongitudinal 274 
-quasitransverse 274 
polarization vectors 265, 278, 287 
-normalization condition 265 
-orthogonality condition 265 
pulse transmission experiments 280 
pulses 323, 325 
-diffusive propagation 323 
quasimomentum density 283, 284 
resistive processes 311 
scattering 287 
-mean free path 292 
-processes 281 
scattering by isotope impurities 334, 
345 
scattering by point mass defects 302, 
277 
-BKE (Boltzmann kinetic equation) 
277 
-distribution function: rate of change 
270 
Subject index 529 
Phonon 
scattering by point mass defects 
-energy conservation law 268 
-transition probability density 269 
-violation of quasimomentum 
conservation law 268 
slowness 275 
slowness surface 275 
source 281,282 
-monochromatic 282 
-Planekian 282 
-point 282 
spectral function 128 
spectrum of relaxation rates 290 
states time reversed 342 
surface of constant frequency 275, 
284, 286 
-curvature of it 276 
-principal curvatures 276 
-solid angle 276 
-surface element 276 
thermal 325 
thermalization of heat pulses 292 
three-phonon interaction spectrum of 
collision rates 291 
wave packets 279-281 
-representation of 270 
Phonons 110 
generated at boundaries 279 
generated inside crystalline specimen 
279 
Planck function 273, 289 
Planckian phonons 282 
Pocket gap modes 143, 189 
Pocket mode stress coupling coefficients 
201 
Point mass defects: random variable 
distribution function of 267 
Fourier transform of 267 
Polarization dyad 278 
Polarization vector 274 
Probability density of transitions per unit 
time 271 
Propagation tensor 274 
QD (quadrupolar deformability) model 
200 
Quadratic variational function 93, 131 
Quantum fluctuations 95 
Quantum mechanics 
canonically conjugated variables 336 
time reversal operation 336 
time-reversal invariance 336 
Quantum Monte Carlo method (QMC) 
87, 110, 116-121, 132 
Quantum relaxation functions 123 
Quantum renormalization parameter 91 
Quantum solids 248 
Quasi harmonic frequencies 118 
Quasielastic central peak 181 
Quasiharmonic lattice dynamics 131 
Quasimomentum 
conservation law 269 
density current 283 
Radio frequency 
dielectric constant measurements in 
KI:Ag + 168 
signature 167 
spectra 168 
Raman polarization selection rules 180 
Raman scattering 179 
Raman spectra polarized 180 
Random element isodisplacement model 
373 
Random variable canonical distribution 
function 327 
Rayleigh characteristic time 324 
Rayleigh's theorem 208 
RbCI:Ag + 168 
RbI 173 
Reactivation of samples 175 
Realistic potentials 147 
Recursion method 377 
Reflectivity coefficient 148 
Regime of relaxation 
collision dominated 302 
collisionless 302 
Reorientationalrelaxation time 169 
Resolvent 296 
Resonant and gap mode strengths 165 
Resonant modes 141 
Rotating wave approximation (RWA) 143, 
209, 210 
Rotational motion in the off-center 
configuration 172 
530 Subject index 
Scattering 
advanced density matrix 342 
by SIAs 291 
detailed balancing condition 345 
differential cross-section 335 
function 121 
of phonon wave packets by SIA's 
271 
of phonons 263 
principle of detailed balance 346 
principle of microreversibility 344 
probability density of transitions 334 
retarded density matrix 343 
tensor 297, 316, 318 
-symmetry properties 316, 318 
transition probability density per unit 
time 343, 344 
vector 121 
Scattering theory 
density matrix of composite systems 
329 
density matrix of the beam 329 
density matrix 329 
Liouville equation 329 
probability density 329 
probability of transition 332 
retarded density matrix 330 
thermodynamic limit 333 
Second-order theory 98 
Self-consistent phonon theory 93, 131 
improved 111, 132 
-free energy 96 
of 1st order (SC1) 9, 92, 95-97, 110, 
111, 116, 125, 130, 132 
Shell model 142 
Short-range correlations 132 
Silver halide clusters 178 
Sine-Gordon model 109 
Sine-Gordon potential 90 
Single particle model 20-25 
Single particle anharmonic oscillator 19 
Slowness vector 284 
Smeared force constants 96, 98, 101, 106 
Smeared potentials 93, 111, 132 
Soft mode behaviour 128 
Solid argon 16 
Solid He 144 
Solid xenon 17 
Solid-liquid-gas interfaces 16 
Soliton 145 
Sources of phonons 
fixed 281 
monochromatic 281,282 
movable 281 
Planckian 281 
Specific heat 110 
Specimen boundaries 280 
Spectral density 52 
Spectral function 120, 122, 130, 131 
Splittings isotope 190 
Stark effect pocket gap mode difference 
spectrum 202 
Stark shifts 200 
Static correlation functions 120 
Static distortions 231 
Static lattice contributions 118 
Stress coupling coefficients 151 
of the IR-active gap and resonant 
modes 198 
Stress shifts 143 
Superlattices 418, 419 
Surface of constant frequency 
flattenning points 286 
Gaussian curvature 286 
local geometric characteristics 286 
parabolic point 286 
Susceptibility 126, 128, 129 
Tensor of fourth rank 289 
basic 298 
material 289 
Tensorial basis 289 
Termination 57, 58, 63, 64, 69-71 
Termination procedure 128 
Thermal excitations of ILMs 249 
Three-body forces 106 
t-matrix approximation 375 
Time reversal operation 271 
Time-dependent correlation functions 120 
Time-dependent quantum Monte Carlo 
method 52-64, 69-71 
Toda lattice 110 
Toda potential 238 
Transfer matrix 109, 110 
Transition probability 269 
density per unit time 268 
per unit time 328 
Translational motion 220 
Transmission coefficient 148 
Trial action 87, 99 
Subject index 531 
Trial free energy 88, 92 
Trial partition function 88 
Trial potential energy 100 
Triatomic molecule 231 
Trotter identity 6-8, 21, 25-27, 30-32, 
36, 45, 66 
Two different elastic configurations 169 
Two-elastic-configuration model 165 
Two-configuration arrangement 166 
Two-configuration model 172 
Two-phonon difference band processes 
160 
Two-phonon difference process 147 
Unfolding technique 195 
Uniaxial stress 151, 198 
UV absorption spectrum 177 
Variational procedure 87 
Variational techniques 6 
Vegard relation 173 
Vertex model 8 
Virial theorem 108 
Virtual crystal approximation 355, 372 
Voigt functions 195 
Wave packets of phonons 279 
Wigner expansion 93, 130 
Wigner solid 9, 43 
Xe 112 
Yttrium-aluminium garnets 323 
containing rare earth atoms 323 
Variational approximations 65-69 
Variational function 88, 90, 126 
ZBM instability 228 
Zero phonon line 159