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

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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

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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