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Conclusions
As I already mentioned in the Introduction, the main target of the present book isto bridge a gap between different communities working in condensed-matterphysics and first of all between the low-temperature community and solid-statecommunity. I would like to stress that though the field of condensed-matterphysics is not a modern one (it was effectively started in 1950-s, 1960-s) it is farfrom being complete. It is permanently enriched by the flow of ideas coming fromdifferent fields stretching from high-energy physics, atomic physics and quantumoptics to biophysics, quantum chemistry and material science. Moreover, there area lot of unresolved interesting problems in the field.
Let us mention some of them which are the bit close to the content of my book:
1. The search for supersolidity in quantum crystals and the nature of rougheningtransition on the phase-interface between quantum crystal and superfluid.
2. The problem of quantum melting of the vortex lattice in rapidly rotating Bose-condensates and the possible analogies with the physics of Quantum HallEffect.
3. The formation of three-particle and four-particle complexes in rotatingsuperfluids and in anion physics.
4. BCS-BEC crossover close to unitarity and the search of Bose-condensation innew materials such as magnons, excitons, polaritons and so on.
5. The search for fermionic and bosonic superfluidity in new systems including2D and 3D 3He–4He mixtures, new phases of 3He in aerogel, p-wave quantumgases and so on.
6. The problem of chiral anomaly in superfluid 3He-A and the nature oftopological phase-transition in unconventional (anomalous) superconductorsand superfluids with Dirac nodal points or lines in the superconductive gap,including topological insulators and recently discovered graphene.
7. The nature of superconductivity in high-TC materials and the nature ofanomalous normal state especially in a pseudogap regime. I would say that thepowerful support of quantum field theorists is required here.
M. Yu. Kagan, Modern Trends in Superconductivity and Superfluidity,Lecture Notes in Physics 874, DOI: 10.1007/978-94-007-6961-8,� Springer Science+Business Media Dordrecht 2013
539
8. Mesoscopic effects in strongly-correlated electron systems including thenature of the heavy mass, anomalous transport properties and nanoscalephase-separation in mixed valence compounds.
9. Different experimental realization of quantum qubits and investigation ofquantum noises. Interplay between localization and interaction in the low-dimensional systems.
10. The nature of low-lying magnetic excitations in the low-dimensional magneticsystems on frustrated lattices including spin ice.
There are a lot of other interesting unresolved problems especially on the borderbetween condensed matter and quantum field theory, in mesoscopic physics andlocalization theory, in quantum turbulence and soft condensed matter, in thephysics of amorphous solids and alloys and so on. There are also a lot of importanttopics which are more close to applications such as nanocomposites andmetamaterials, photonics and plasmonics, physics of polymers, and physics ofsmall electron devices.
Thus I would like to encourage the young researches who started their careersin condensed-matter physics to stay in the field and to establish their leadership.
540 Conclusions
Index
AAction
Haldane effective action, 145supersymmetric hydrodynamic action, 117,
123, 126–128, 136, 143AFM background, 200, 422, 473, 476AFM string, 200, 274, 399, 405, 416, 422, 475Alkali elements (Li, Na, Rb), 51, 153, 154,
292, 368, 369Alkaline-like elements (Ca, Ba, Sr), 464Angles
Brewster angle, 98, 99, 101transcritical angle, 80, 81, 86, 102, 114
Anomalychiral anomaly, 117, 126, 135, 139,
142–144, 258Kohn’s anomaly, 294, 297, 298, 303, 316,
318, 340, 353, 362, 400Approximation
Kanamori T-matrix approximation, 308,327, 438
local density (LDA) approximation, 335one-channel approximation, 154, 167, 177,
200random phase approximation (RPA),
321–323, 335, 501resonant approximation, 167, 175Thomas-Fermi approximation, 161, 306,
321Atomically rough surfaces, 66, 68, 95, 96Atomically smooth surfaces, 66, 68, 70, 72,
73, 75, 91, 96, 114
BBardeen, Cooper and Schrieffer (BCS)
BCS-type of superfluidity, 118, 119BCS-type of superconductivity
BCS critical temperatureBCS-domain, 168, 169, 173, 174, 177, 178,
223, 228, 230, 231, 236–238, 240, 244,249, 252, 254, 258
BCS-BEC crossover, 153, 174, 182, 205, 215,223, 224, 229, 236, 238, 241, 248, 249,260, 272, 275, 416, 419, 423, 424
Berezinskii-Kosterlitz-Thouless (BKT) criticaltemperature, 238
Berry phase, 142, 481, 482Bethe ansatz, 400Bi6s–O2pr bonds, 276, 277Bogoliubov coefficients, 403Bohr magneton, 125, 321, 361, 369,
508, 519Boltzman gas, 10Bose
Bogoliubov Bose gas, 403Bose (Fermi) cluster, 403Bose gas, 174, 181Bose solid, 61, 194
Bose Einstein condensation (BEC)BEC critical temperature, 423BEC-domain, 169, 171, 177
Bosonscomposed bosons, 119, 153, 164, 170, 178,
200, 204, 216, 224, 230, 235,237, 264
Schwinger bosons, 199slave bosons, 198, 399, 402
Brillouin zone, 303, 441, 493
CCapillary effects
Capillary constant, 103, 357Capillary waves, 69, 87, 89, 95
Cartan form, 121
M. Yu. Kagan, Modern Trends in Superconductivity and Superfluidity,Lecture Notes in Physics 874, DOI: 10.1007/978-94-007-6961-8,� Springer Science+Business Media Dordrecht 2013
541
Cartesian coordinates, 26, 157Channel
closed channel, 165, 168, 177Cooper channel, 171, 173, 188, 225, 241,
298, 307, 316, 324, 339, 342, 371open channel, 165, 168particle-hole (SDW) channel, 304, 370
Charge density wave (CDW), 275, 403Cherenkov effect, 80, 113Coefficient
sound reflection coefficient (R), 100, 101sound transmission coefficient (D), 80, 81,
98, 101, 112Collapse (in the attractive bosonic system),
200Collisions
dimer–dimer collisions, 219dimer-fermion collisions, 206, 207, 219
ComplexBiL2O6 complex, 276, 277, 279BiO6 complex, 276, 277, 279, 280octahedral complex, 275, 276, 278, 283
Componenthyperfine component, 164, 248, 367, 369normal component, 4, 5, 14, 21, 31, 41, 47,
51, 159superfluid component, 14, 16, 21, 27, 40,
93Composite holes, 182, 274, 399, 416, 422–424Compound
BaKBiO compound, 280FeAs-based compounds, 293
ConditionsconductivityDrude conductivity, 451flatness conditions, 121Hall conductivity, 145Mott-Regel minimal conductivity, 452optical conductivity, 273, 277
Confinementconfinement, 182confinement in quark-gluon plasma, 182confinement in slab geometry, 182
Conservation laws, 3, 4, 6, 16, 28, 52, 81, 122Cooling
evaporative cooling, 153, 156, 158, 197laser cooling, 154, 155
Cooperon, 330Criterion
Landau criterion for superfluidity, 49, 63Landau-Thouless criterion, 172, 174, 270,
340
Lindemann criterion, 38, 57Migdal (quasiclassical) criterion, 162, 178,
373Critical angular velocities XC1, XC2, 4, 22, 24Critical magnetic fields HC1, HC2, 4Cuprates
optimally doped cuprates, 305underdoped cuprates, 144, 182, 272, 275,
399, 464Curie law, 357, 437Curie temperature, 362, 465, 476, 521, 532Curie-Weiss constant, 533Current
anomalous spin current, 145axial current, 141orbital current, 119
D2D gas of kinks, 70, 74de Boer parameter, 57–59, 64Debye shell, 349, 358Debye-Waller factor, 59Defectons, 60, 62, 66Diagrams
exchange diagram, 205, 339ladder diagrams, 226, 437skeleton diagrams, 299
Dielectric permittivity (dielectric constant e),307, 310, 321, 323
Difermionic molecules, 118Diffusion coefficient (D), 44, 104, 111, 350,
458Dihalcogenides (TaS2, TaSe2), 323Dimer, 153, 170, 181, 203, 205, 206, 208, 210,
216, 219Dirac
Dirac lines, 117Dirac points, 117Dirac spectrum, 117
Displacement tensor, 83, 84Distortions
breathing distortion, 276rotational distortion, 280tilting distortion, 276
Distributionbimodal distribution, 159, 178Bose–Einstein distribution, 159Fermi-Dirac distribution, 171, 252, 294,
329, 453, 493Maxwell distribution, 153, 157
542 Index
EEffect
Altshuler-Aronov effect, 458, 459de Haas-van Alphen (dHvA) effect, 338Efimov effect, 181, 182, 207, 209, 210electron-polaron effect (EPE), 325, 335,
450, 459Josephson effect, 63, 88, 97, 146Kohn-Luttinger effect, 294Meissner effect, 320, 321, 323quantum Hall effect: integer (IQHE);
fractional (FQHE), 39, 145, 323, 539Zeeman effect, 154, 155, 157, 159, 522
Einstein relation, 455Elastic modulus
bending elastic modulus, 31compression elastic modulus, 31, 32shear elastic modulus, 31
Elliptic integral of first and second order, 186Energy
Fermi-energy (eF), 170, 230, 293, 318, 362,405
Ginzburg-Landau Free-energy, 125recoil energy, 156Zeeman energy, 522zero-point energy, 59
EquationBethe-Salpeter (BS) integral equation, 125,
172–174, 188, 202, 224, 225, 241, 259Bogoliubov-de Gennes (BdG) equationm,
136, 138, 143Dirac equation, 117, 135, 136, 138, 139,
143, 144Dyson equation, 226, 269Gross-Pitaevskii equation, 19, 24, 37Josephson equation, 88, 97Leggett equations, 223, 224, 231, 232,
249–251, 260Lippman-Schwinger integral equation,
168, 169Schroedinger equation, 37, 38, 47, 213Skorniakov-Ter-Martirosian (STM) inte-
gral equation, 181, 205Excitation
collective excitations, 4, 35, 117, 125, 126,145, 182, 215, 223, 236, 241, 244, 258,261
fermionic excitations, 245, 246Experiment
ARPES experiments, 338Andronikashvili experiments, 4, 20, 21, 65diffraction experiments, 159, 161, 178, 532EXAFS experiments, 263
Raman scattering experiments, 285STM experiments, 273, 508
FFaceting transition, 70, 71Fermi
Fermi-gas, 118, 119, 125, 153, 154, 161,163, 168, 170, 175–178, 182, 200, 205,219, 223, 224, 226, 228–231, 236–239,241, 246, 260, 267, 268, 274, 286, 291,293, 296–301, 315–319, 321, 332, 347,348, 352, 353, 356, 357, 359–361, 367,369, 387, 388, 398, 400–403, 415, 419,431, 432, 434, 435, 436, 438, 448, 449,461
Fermi-liquid, 118, 134, 143, 278, 280–282,285, 320, 338, 347, 348, 354, 364, 365,386–388, 397, 399, 402, 404, 405, 416,424, 431, 432, 438, 439, 447, 449, 451,453, 457, 461
Fermi momenta, 316, 339Fermi surface, 128, 252, 265, 303, 306,
321, 322, 336, 338, 348, 349, 382, 393,402, 403, 421, 431, 433–436, 439
Fermionschiral fermions, 139, 140, 143composed fermions, 164, 181, 182, 200,
202–204Majorana (massless) fermions, 127, 146
Ferronsbound ferron, 482‘‘coated’’ (bare) ferron, 483, 484, 486, 487ellipsoidal (spherical, circular) ferron, 477,
478, 506orbital ferron, 465, 504–506temperature ferron, 466, 476, 536
Feshbach resonance, 51, 117, 119, 125, 153,154, 159–161, 164, 165, 167, 168,175–177, 181, 200, 217, 219, 223, 235,240, 246–249, 258, 274, 292, 368
Few-body systemsFeynman-Onsager quantization of the vortex
lines, 22Field
gradient field, 155Grassman (anticommuting) fields, 128, 132quadrupole magnetic field, 153
FormulaBCS formula, 169, 265Einstein formula, 63, 162, 230, 249, 265,
368Miyake formula, 238, 360, 418
Index 543
Stirling formula, 515Frequency
Cyclotron frequency (XC), 457Larmor frequency, 157, 323Matsubara bosonic (fermionic) frequency,
170, 377, 382NMR frequency, 507
Friedel oscillations, 294, 298, 353, 370Function
anomalous Green’s function (FS), 232,233, 241–243, 389, 392
Airy function, 422Bessel function, 360, 478, 506Lindhard function, 295Mackdonald function, 360, 485Matsubara (temperature) Green function,
171normal Green’s function (GS), 232–235,
368Rieman dzeta function, 377vacuum Green function, 168, 186, 225, 300Yakobi h-function, 38
GGalilean invariance, 7, 16, 30, 81, 131Galitskii-Bloom results, 226, 268Gap
activation (transport) gap, 275, 278, 279,285
correlation gap, 229, 271–273, 275, 283Jahn-Teller gap (EJT), 468, 469, 505optical gap, 275, 277–279, 281, 282, 285,
286pseudogap, 229, 235, 236, 263, 264,
270–273, 283, 421superconducting (superfluid) gap (D), 118,
122, 123, 126, 127, 168, 223, 224,231–241, 246, 250, 251, 257, 372, 377,382, 493
Gas2D gas of kinks, 70, 74Bogoliubov gas, 403Boltzman gas, 10Bose gas, 19, 24, 37, 39, 48, 51–53, 63, 64,
153, 154, 160–162, 170, 174, 178,181–183, 192, 195–197, 199, 200, 216,218, 219, 228, 230, 234, 235, 238, 244,255, 268, 270, 286, 374, 398, 403, 408,414, 415, 419
Fermi gas, 118, 119, 125, 153, 154, 161,163, 168, 170, 175–178, 182, 200, 205,219, 223, 224, 226, 228–231, 236–239,
241, 246, 260, 267, 268, 274, 286, 291,293, 296–301, 315–319, 321, 332, 347,348, 352, 353, 356, 357, 359–361, 367,369, 387, 388, 398, 400–403, 415, 419,431, 432, 434, 435, 436, 438, 448, 449,461
polarized gas, 248, 318, 361, 3862D gas of kinks, 70, 74
Generalized boundary conditions, 81, 87, 103,107, 114
Ginzburg-Landau functional, 61, 274, 375Goldstone
Goldstone massless modes, 3, 5, 6, 12, 18,117, 121–123, 127, 128, 146, 259, 397
fermionic Goldstone, 117, 123, 127, 128bosonic Goldstone, 123
Goodenough rules, 405Gradient expansion, 85Grafoil, 347, 354, 357, 363–365Group
lattice symmetry group D4, 185renormalization group (RG), 3033D rotation symmetry groupSU-5 (SU-2, U1) symmetry group
Growing and melting shapes of the crystals, 68Growth coefficient (Kgr), 79, 89, 91–94, 104,
105, 108, 110–112, 114Gutzwiller constraint, 61
HHall-Vinen friction coefficients (b, b’), 4, 28,
142Hamiltonian
hamiltonian of the attractive-U fermionicHubbard model, 264
hamiltonian of the Bose-Hubbard model,299
hamiltonian of the double-exchange model,469
hamiltonian of the Fermi-Bose mixturemodel, 374
hamiltonian of the Shubin-Vonsovskymodel, 307, 308
hamiltonian of the two-band Hubbardmodel, 325
Heisenberg hamiltonian, 4063He-4He solution
liquid solutions, 103solid solutions, 103, 362
3He-Amoderately clean 3He-A, 144superclean 3He-A, 140, 144
544 Index
Heavy mass, 334, 335, 337, 340, 342, 453, 540Heterostructures GaAs-AlAs, 323Holon (biholon), 181, 182, 198, 199, 201, 275,
397–399, 401–403, 408, 411, 412, 415,416, 422
Hooge constant (aH), 524, 525, 535Hund’s coupling (JH), 344, 469Hydrodynamics
bosonic hydrodynamics, 127hydrodynamics of fast rotations, 5, 40,
42–44, 46, 47, 53hydrodynamics of slow rotations, 4, 28, 33,
39–41, 46, 47, 49orbital hydrodynamics, 53, 117–119, 145,
258superfluid hydrodynamics, 3, 5, 15, 19, 20,
62, 117, 120, 124–126, 139, 142, 144supersymmetric hydrodynamics, 117,
126–128, 136, 143
IIdentity
Mermin-Ho identity, 121, 142Ward identity, 259
Impuritymagnetic impurity, 466non-magnetic impurity, 466
Impuritons, 62Inertial mode, 11–13, 35Instability
Kelvin-Helmholtz tangential instability, 95Insulator
CDW-insulator, 275topological insulator, 539
Integrationangular integration, 193, 209, 211frequency integration, 233, 234
Interactiondipole–dipole interaction, 182electron-phonon interaction, 264, 348electroweak interaction, 127Hubbard interaction (U), 175, 196, 201,
202, 300, 325–328, 332, 341, 376, 418RKKY interaction, 294
Irrotational flows, 7Isotope
fermionic isotope, 154, 292bosonic isotope, 154
JJastrow macroscopic W-function, 60Josephson arrays, 184
KKapitza thermal resistance (RK), 79, 80, 102,
107, 108, 112, 114Kondo singlet, 398, 473Kronecker symbol, 483
LLadder
two-leg ladder 403, 405–410, 424three-leg lader, 397, 398, 403, 410, 411,
413, 415, 424Lagrangian
infrared Lagrangian, 127Lagrangian of electroweak interactions,
127Landau gauge, 38, 126Landau-Tissa two-velocity superfluid
hydrodynamics, 3Lande factor (g), 321, 530, 532Laplace operator, 422, 474Larmor orbit, 157, 323Latent heat, 58Laughlin incompressible liquid state, 39Legendre polynomials, 173, 515Level
anomalous level, 141surface Andreev levels, 354Tamm surface levels, 354Zeeman sublevels, 157zeroth Landau level, 137–140
Levi-Civita tensor, 121Limit
paramagnetic limit, 125, 126, 320, 361,385, 388, 392, 393
solubility limit, 275, 281, 351unitary limit, 165, 167, 170, 223, 230, 231,
234, 235, 237, 248, 249, 335, 342Localization
Mott-Hubbard localization, 62, 175, 310,491, 500
Verwey localization, 310, 311, 491, 492Long range order
diagonal long range order (DLRO), 60off diagonal long range order (ODLRO), 60
Lord Kelvin (Thomson) bending oscillations, 4Luther-Emery liquid, 405, 415Luttinger liquid, 354, 364, 399, 401–404, 415,
431, 432, 449
MMagnetic number, 193, 318Magnetoresistance
Index 545
Magnetoresistance (cont.)colossal magnetoresistance (CMR), 325,449, 450, 460, 463–465, 467, 489, 490, 513giant magnetoresistance (GMR)tunneling magnetoresistance (TMR), 519,
530Majorana flops, 157, 158Marginality, 292Matrix
CO checkerboard insulating matrix, 310dimer-dimer scattering matrix (T4), 213three-particle T-matrix (T3), 211, 215
Matrix elementsdiagonal matrix elements, 108, 338off-diagonal matrix elements, 108
Maxwell construction, 194, 342, 498, 500Measurements
ARPES measurements, 272inelastic neutron scattering measurements,
284, 286Melting-crystallization processes, 68, 69, 80,
86Melting-crystallization waves, 57, 67–70, 73,
75, 76, 79, 80, 87–90, 94, 95, 98, 102,109–111, 114
Melting of the vortex lattice, 5, 35, 38, 539Metal
nobel metals, 306semimetals, 306, 323
Miller indices, 75Mixture
Fermi-Bose mixture of 3He and 4He, 204,274
Fermi-Bose mixture of 6Li and 7Li, 267,373
disbalanced Fermi-Bose mixture, 218, 219space separated Fermi-Bose mixture, 263,
275strongly interacting mixture of spinons and
holons, 182, 415Mobile phase-interface, 67, 93, 114Mode
Engelbrecht-Randeria mode, 439, 448, 449longitudinal stretching mode, 284, 286zero-mode, 117, 137, 138, 140
Modelanharmonic models for high-TC materials,
282jelly model, 305–307Kondo lattice model, 465, 469, 490, 491,
501, 504t-J model (bosonic, fermionic), 181, 182,
184, 194, 195, 198, 199, 274, 344, 359,
397–401, 404, 406, 407, 410, 414,416–424, 465, 473, 505, 506
Tomonaga-Luttinger model, 400two-channel Feshbach model, 275
Momentrelative orbital moment (l), 126, 224, 246,
247total rotating moment (J), 293
Monte Carlo simulations, 231, 235Mott’s law, 280
N1/f- noise, 513, 518, 519, 523–526, 535, 540Nagaev-Mott solution, 475Nagaoka theorem, 501Narrow band, 280, 299, 315, 324, 326, 327,
338, 340, 343, 449, 450, 456, 460, 461,513
Neel temparture (TN), 466, 536Negative compressibility, 338, 471Negative-U centers, 264, 274Neutron diffraction data, 276Non-classical rotation inertia (NCRI), 65Nonlinear elasticity theory, 4, 25, 39Nozieres-Schmitt-Rink scheme, 234Nyquist-Johnson white noise, 526
OOccupation
double occupation, 196, 505single occupation
Octahedronrigid octahedron, 276soft octahedron, 276
Ohm’s law, 523Onsager relations, 44Orbital
antibonding orbital, 277bonding orbital, 277nonbonding orbital, 277
Orthogonality catastrophe, 338, 432Overdamped modes, 144
PPairing
bipolaronic (biexcitonic) pairing, 192non-diagonal pairing, 199(singlet) s-wave pairing, 165, 173,
186–188, 190, 234, 238, 248, 249, 253,261, 267, 292–294, 311, 320, 322, 340,
546 Index
343, 347, 350, 351, 353, 359–361, 363,367, 369, 417, 418, 424
(triplet) p-wave pairing, 134, 173, 185, 186two-boson pairing, 181, 184, 192, 194,
198, 200, 202, 417two-holon pairing, 181, 199
PairsCooper pairs, 118, 122, 125, 153, 164, 165,
182, 231, 238, 245, 246, 258, 265, 273,320, 369, 371, 387
local pairs, 118, 119, 123, 153, 165, 170,192, 193, 197, 224, 231, 264, 272, 277,283, 419, 421
preformed pairs, 421vortex-antivortex pairs, 238
ParameterBorn parameter, 169, 237gas parameter, 164, 223, 226, 230, 235,
240, 245, 248, 249, 251, 265, 272, 274,292, 296, 298, 300, 309, 318, 322, 330,332, 337, 353, 374, 380, 432
Lindemann parameter, 58, 59parameters of the double-well potential,
284Part
imaginary part (Im), 19, 79, 110, 189, 247,330, 332, 404, 431, 439, 443, 449, 451,454
real part (Re), 110–112, 176, 250, 331regular part, 294singular part, 435, 437
Pauli principle, 162, 207, 215, 318, 362, 372Perovskite manganites, 490, 492, 523Phase
axial phase, 145, 251, 368, 375, 393, 394k, g, b, r3 phases, 390, 391BCS A (B)-phases, 123, 253Bosonic A-phase, 123, 125, 137distorted cubic phase, 376orthorhombic phase, 278phase of normal bosonic metal, 263
Phase coherence, 284, 285Phase-diagram, 58, 60, 125, 144, 198, 204,
205, 219, 223, 224, 230, 248, 264, 266,302, 310, 311, 367, 403, 411, 413, 417,421, 463, 473, 507
Phase-transitionquantum phase-transition, 146, 234topological phase-transition, 146, 234, 248,
539Phonon mismatch theory, 102Photonics, 540
Photonsleft-moving photons, 155right-moving photons, 155
Physicsphysics of glasses, 264physics of quantum gases, 181, 539
Planebasal plane, 489, 490, 492BiO2-plane, 281
PlasmaCoulomb plasma, 306, 321quark-gluon plasma, 182, 183, 422, 476
Plasmonics, 540Plumbates-bismuthates BaKBiO-BaPbBiO,
263Point
quantum critical point, 252k-point behavior, 286Poisson brackets, 4, 39Polarization operator (G), 294–296, 298, 303,
316, 317, 337, 371, 382, 384, 434, 437Polariton, 539Polaron
spin-polaron, 182, 274, 399, 421, 423, 424,464
Polenorth (south) pole of the Fermi-surface,
265, 303, 306, 321, 322, 336, 338, 382,393, 402, 421, 431, 439
pole of the total vertex, 175Potential
centrepertual effective potential, 208a-decaying potential, 166parabolic confining potential, 154string-like confinement potential, 182
Projection operator (P), 469, 491, 505Proximity effect, 58, 342Pseudospin operator (s), 505
QQuantum
quantum chromodynamics (QCD), 183,399, 476
quantum crystals, 39, 57–59, 61, 62,66–68, 539
quantum electrodynamics (QED), 117,135, 172, 225
quantum hydrodynamics, 76, 117quantum liquids, 76, 246quantum nucleation, 91quantum permutations, 61
Index 547
quantum qubits, 540Quartets
extended quartets, 195, 197, 200, 204, 216,218, 220
local quartets, 197
RRadius
Bohr radius (aB), 306, 307, 310, 321, 323correlative radius (rS), 306, 501hyperradius, 208ionic radius, 276, 307
Rainer-Serene strong-coupling corrections,367, 380, 384
Ranninger term, 177Rayleigh-Stonely waves, 70Rayleigh waves, 57, 69, 70, 76, 79, 87, 96, 98,
102, 109, 113, 114Recrystallization displacements, 69, 83, 84,
100, 109Recrystallization rate (n), 69, 83, 91, 96Regime
ballistic (Knudsen) regime, 10, 140, 141,143
hydrodynamic regime, 40, 105, 138–141,143, 144, 183
regime of Varma’s valence skipping, 263Reflection
Andreev reflection, 273mirror reflection, 99
Relationsanticommutation relations, 128, 131commutation relations
Relaxation rate, 219Relaxation time, 53, 112, 113, 355, 362Representation
irreducible representation, 185diagrammatic representation, 206, 214
ResonanceAFM resonance, 507broad (narrow) Feshbach resonance, 167,
175, 176, 200p-wave (s-wave) Feshbach resonance, 223,
246–248g-resonance, 272, 273
Riplons, 69, 357Roughening transition
classical roughening, 66quantum roughening, 57, 74
Ruthenates (Sr2RuO4), 117, 291, 292, 343
SSector
gauge-orbital sector, 126, 146spin sector, 146
Separationnanoscale phase-separation, 463, 472, 473,
478, 491, 540spin-charge separation, 181, 182, 198, 199,
397, 399, 401, 402, 421, 422, 424Shift
Hartree–Fock shift, 183, 189, 194Wick shift, 232, 271
Singularityinfrared singularity, 126Van Howe singularity, 303
SolutionAbrikosov solution, 38parquet solution, 304
SpectrumBogoliubov quasiparticle spectrum, 403hyperbolic spectrum, 303spectrum of orbital waves, 117, 122, 124,
125, 135, 143, 144, 258Spectroscopy
gap spectroscopy, 240infrared spectroscopy, 338
Spinelectron spin (S), 154, 166, 198, 307, 369-
372, 374, 416, 473, 520, 521nuclear spin (I), 154, 367, 369, 371, 372total spin (J),,125, 154- 156, 182, 185, 224,
246, 258, 292, 369, 388, 412, 469, 472,504
Spin bags, 464Spin ice, 540Spinon, 181, 182, 198, 201, 275, 379, 399,
401- 403, 411, 412, 415, 416, 422Splitting
dipolar splitting, 248gradient splitting, 155Zeeman splitting, 154, 155, 369
Stateantibound state, 187, 332, 438, 439, 441-
443, 447- 449edge state, 146insulating state, 282, 491, 500, 535shallow bound state, 154, 165, 167, 170,
176, 182, 197, 212, 237, 360, 423virtual state, 167, 182, 203
Stratification curves, 103Stress tensor, 69, 82, 85, 87, 105, 108, 114
548 Index
Stripes, 405, 463, 464, 507- 509Submonolayer
submonolayer of 3He, 145, 354, 356, 357,364, 375, 437
2D 4He submonolayer, 184Superlattices (PbTe-SnTe), 343Susceptibility
particle–particle susceptibility, 171, 269Pauli susceptibility, 437spin susceptibility, 273, 356, 405, 406, 432
Superconductivityhigh-TC superconductivity, 198, 291, 347,
354, 364, 416Superconductors
anomalous superconductors, 246, 539organic superconductors, 291, 323
Superflow of defects, 66Superfluidity
resonance superfluidity, 224, 247, 261Superplasticity, 66Supersolidity, 22, 39, 57, 58, 60, 64- 66, 76,
196, 539Surface
surface diffusion, 105, 109surface elasticity, 81, 101surface hydrodynamics, 69, 79- 81, 85, 93,
102, 103, 114surface kinetic coefficients, 79surface rigidity (surface stiffness), 69, 73,
74, 101, 103surface tension, 69, 79- 81, 85, 89, 354,
357
TTangential flow, 79, 93, 95, 114Technique
diagrammatic technique, 124, 144, 210,258, 421, 456
functional integral technique, 144Temperature
degeneracy temperature (To), 153, 160,161, 177, 188, 197, 201, 203,219, 266
Saha (crossover) temperature (T*), 193,203, 204, 218, 224, 228, 238, 263, 268,360, 368, 419
temperature jump (DT), 107–109, 113Texture
bending texturetexture of the l-vector, 121, 125, 138twisted texture, 136, 138, 144, 146
Theory
Anderson-Bogoliubov theory for collectiveexcitations, 241–246
Anderson-Brinkman-Morel (ABM) spin-fluctuation theory, 384
Andreev-Lifshitz theory, xxii, 57, 61, 66,79, 91
Bardin-Baym-Pines (BBP) theory, 347,350
Fisher-Hohenberg theory, 192, 195, 204,238
Heitler-London theory, 165Thermodynamic potential (X), 378, 437, 447,
449Thomas-Fermi wave vector, 306, 321Threshold
percolation threshold, 278, 280, 282, 502,504, 508, 514, 517, 519, 525, 526, 535
threshold of absorbtion, 168, 178, 240Time
lifetime, 144, 163, 164, 166, 176, 205, 219,247, 362, 372, 388, 431
scattering time, 9, 30, 106, 182, 205, 219,237, 322, 449–451, 454–459
Tkachenko modes, 4, 53Topological charge (Q), 146Topological invariant, 27, 145Transformation
Bogoliubov (u-v) transformation, 63, 128Hubbard-Stratonovich transformation, 199
Transitionlocalization transition, 175, 479metal-insulator transition, 299, 466, 526
Trapsdipole traps, 153, 159, 164magneto-optical traps, 153, 154, 177, 368quadrupole traps, 156–158
Tunneling probability, 517
UUemura plot, 421Umklapp processes, 4, 5, 30, 40, 41, 54, 110,
273, 452, 453
VVacancies
surface vacancies, 62, 75thermo-activated vacancies, 64zero vacancies, 57, 61–64, 72
Vacancions, 60, 62, 63van der Waals attraction, 183, 184, 186, 187,
274, 348, 352, 355–357, 360
Index 549
Variable-range hopping, 280Vector
l-vector, 121, 122, 125, 136, 138nesting vector, 272, 303
Velocityvelocity circulation, 24normal velocity (vn), 53, 124, 139, 142superfluid velocity (vs), 16, 19, 22, 23, 42,
49, 82, 88, 100, 118–121, 124Vertex
irreducible bare vertex (Ueff), 173, 174,225, 295, 307, 309, 339, 342
total vertex (C), 173, 175, 202, 259, 382,384
Verwey charge ordering, 489Verwey localization, 310, 491, 492Vicinal surfaces, 75, 114Viscosity
first and second viscosity coefficientsorbital viscosity, 143, 144viscous stress tensor, 108
Vortexsingular vortex, 142, 144
Vortex lattice
triangular vortex lattice in superfluid 4He,4, 5
triangular vortex lattice in type-II super-conductors, 25, 26
WWaves
charge density wave (CDW), 275, 397,398, 402, 403
orbital waves, 117, 122–127, 135, 143,144, 146, 258, 259
radiofrequency waves, 168, 240Width
natural linewidth, 155, 156resonant width, 166
ZZero-point steps, 72Zhang-Rice singlet, 473Zigzag magnetic chain, 464
550 Index