Fujita S., Ito K., Godoy S. Quantum Theory of Conducting Matter

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Index 245

Equal numbers of ±pairons, 37, 41, 56, 59,

113, 114, 126, 165, 208, 215, 219

Equation-of-motion method, 41, 45, 50, 59,

60, 165

Factorization, 54, 135

Fairbank, 4, 115

Fermi anticommutation rule, 10, 22, 47, 52, 62,

65, 79, 233, 234

Fermi distribution function, 54, 99, 186

Fermi sea, 75

Fermi surface, 10, 12, 27, 29, 30, 42, 43, 75,

77, 78, 89, 111, 114, 125, 159, 160, 161,

162, 163, 166, 167, 173–178, 181, 183,

184, 185, 189, 190, 193, 194, 195, 196,

204, 205, 210, 212, 219, 222

Fermi temperature, 166, 183

Fermi velocity, 19, 75, 87, 88, 114, 166, 167,

219, 222

Feynman, 22, 23, 24, 32, 34, 61, 70, 146, 147,

149, 154, 214

Feynman diagram, 22, 23, 24, 32, 34

Floating magnet, 1, 2

Fluxoid, 123

Flux quantization, 1, 3–4, 6, 12, 13, 41, 103,

106, 108, 113–129, 146, 157, 211, 219, 220

Flux quantum, 4, 104, 106, 147, 220

ohlich, 15, 19, 22, 23, 209, 210

ohlich Hamiltonian, 15, 19, 22, 210

ohlich interaction Hamiltonian, 23

Fugacity, 81, 82

Full Hamiltonian, 73–75

Gap, 6, 7, 11, 12, 36, 37, 38, 39, 40–41, 45–60,

79, 89, 90, 91, 92, 95, 96, 97, 100, 101,

126, 131, 133, 136, 137, 140, 165, 170,

209, 211, 212, 213, 216, 221

Gap equation, 36, 37, 38, 40–41, 45–60, 137,

165, 211

Gauge-choice, 120

Generalized BCS Hamiltonian, 18, 29, 30, 59,

111, 155, 162, 163, 212, 222

Generalized BCS model, 173, 215

Generalized energy-gap equation, 57

Generalized London penetration depth, 121

Generalized London’s equation, 121

Generalized Ohm’s law, 92, 100

Giaever and Megerle, 7, 90, 91, 98

Ginzburg–Landau equation, 132

Ginzburg and Landau (GL), 105, 131, 132,

133, 134, 135, 136, 138, 139, 140, 152,

153, 154, 208, 209

Ginzburg–Landau Theory, 6, 131–141,

208–209

GL wavefunction, 131, 132, 134, 135, 139,

140, 152, 153–154, 208, 209

Gorter, 207

Gorter–Cassimir’s Model, 207

Grand-canonical-ensemble average, 12, 53

Ground pairon, 11, 33, 34, 42, 60, 92, 124, 125

Ground state, 6, 11, 29–43, 45, 49, 50, 55, 56,

59, 70, 73, 75, 76, 89, 95, 113, 135, 136,

137, 139, 163–165, 169, 210, 211, 212,

215, 216, 219

Ground state energy, 6, 11, 29, 35, 37, 38, 39,

40, 45, 59, 75, 76, 89, 135, 136, 137, 139,

164, 165, 169, 211, 212, 215, 219

Hall angle, 88, 197, 200, 202

Hall coefﬁcient, 88, 173, 174, 176, 181, 183,

184, 197, 199, 201–202, 204

Hall effect, 200, 215–216, 227

Harmonic approximation, 16, 17

Harmonic equation of motion, 20

Harmonic oscillator, 20, 21

Heat capacity, 6, 7, 15, 16, 17, 43, 81, 82, 83,

85, 107, 167, 168, 190, 207, 221

Heavy fermion, 10, 18, 56, 61, 62, 65, 66, 68,

69, 70, 71, 79, 80, 99, 101, 133, 134, 135,

146, 147, 153, 198, 214, 216, 227, 233–234

Heisenberg equation of motion, 234–237

Heisenberg picture, 235

Hermitian conjugate, 22, 235

High critical temperature, 87, 157, 166–168

High-Tc cuprate superconductor, 100, 157, 215

High temperature superconductor, 9, 157–171,

215, 222

Hohenberg’s theorem, 83, 214

“Hole”, 11, 12, 29, 30, 31, 32, 33, 34, 36, 37,

39, 42, 43, 51, 53, 73, 74, 88, 89, 93, 96,

111, 114, 117, 125, 131, 161, 162, 163,

174, 175, 176, 177, 183, 184, 185, 189,

190, 195, 197, 198, 200, 201, 202, 204,

205, 210, 211, 212, 219, 222, 224, 231

“Hole” wave packet, 162, 195

Hyperboloidal Fermi surface, 42, 43, 222

Impurity, 198, 203

Inﬂection point, 181, 184, 189, 190, 195

Instantaneous, 24

Interaction strength, 30, 37, 135, 140, 163,

168, 169, 194, 209, 210

Interference, 5, 12, 143–147, 153, 155,

214, 220

246 Index

Intermediate state, 223, 224

Internal energy density, 81, 84

Interpairon distance, 86, 87, 166, 167, 213, 222

Ionicity, 173, 175, 182, 190

I–V curve, 89, 90, 91, 92, 96, 97, 98, 100, 101,

143, 144, 169–170, 221, 222

Josephson, 1, 4–6, 12, 13, 70, 92, 103, 115,

143–155, 157, 193, 214–215, 219, 220

Josephson current, 5, 146, 147–150, 153

Josephson–Feynman equation, 149, 154

Josephson frequency, 151, 154, 214

Josephson interference, 5, 12, 214, 220

Josephson junction, 4, 5, 143, 144, 146, 147,

153, 154, 214

Josephson theory, 214–215

Josephson tunneling, 4, 92, 143–147, 153,

193, 214

Kinetic theory, 198–202

k-q representation, 63, 74

k-vector, 18, 54, 111, 116, 159, 160, 162

−xSrxCuO

, 174, 182, 183, 199

Landau, 6, 10, 105, 131–141, 183, 184, 188,

208–209, 215

Laser, 5, 12, 115, 116, 143, 146, 147, 153, 155,

214, 220

Lattice-dependent anisotropy, 193

Lattice dynamics, 15–19

Layered lattice structure, 222

Layered structure, 157–160

Linear, 20, 43, 49, 73, 78, 79, 80, 88, 110, 114,

119, 120, 131, 132, 133, 135, 136, 138,

139, 140, 150, 152, 153, 155, 157, 161,

166, 178, 187, 189, 194, 195, 197, 200,

203, 209, 213, 214, 215, 216, 219, 220,

221, 222, 224, 233, 236, 237

Linear dispersion relation, 73, 80, 88, 153, 155,

157, 161, 166, 178, 187, 189, 200, 213,

214, 219, 220, 221

Linearly, 79, 150, 224

Liquid nitrogen, 9

London, F., 86, 119–123, 126, 128, 132, 139,

207–208, 209, 213

London, H., 119–123, 126, 128, 132, 139,

207–208, 209, 213

London–London, 119, 207–208

London rigidity, 208

London’s equation, 113, 119–123, 128,

132, 209

Longitudinal acoustic phonon, 161, 194

Longitudinal optical phonon, 88, 157, 178

Longitudinal wave, 19, 110

Long-range order, 6, 214

Lorentz-magnetic force, 115, 127, 202, 220

Lower critical ﬁeld, 8, 103, 104, 224

Macrowavefunction, 126, 208

Magnetic ﬂux, 1, 3, 4, 5, 8, 12, 104, 106, 122,

123, 136, 138, 145, 146, 149, 220, 224

Magnetic impurity, 198

Magnetic pressure, 1, 106, 127

Magnetic property, 3, 103, 181

Magnetization, 104, 105, 107, 131, 183, 185,

187, 188, 189, 208, 223

Main superconducting property, 103, 157

Major properties of a superconductor, 219

Many-boson state of motion, 114

Markofﬁan approximation, 26, 27

Massless boson, 83, 84, 85, 146, 147, 168,

214, 222

Massless particle, 79, 128

Maximum heat capacity, 85, 168, 221

Meissner, 1–3, 8, 9, 13, 39, 103, 104, 106, 108,

121, 127–128, 136, 157, 207, 219, 220

Meissner effect, 1–3, 8, 13, 39, 127–128, 136,

157, 219, 220

Meissner pressure, 106, 127

Meissner state, 103, 104, 106, 121, 127

Metallic compound, 8

Mixed state, 8, 104, 224

Molar heat capacity, 81, 82, 83, 85

Momentum, 19, 22, 24, 26, 27, 31, 39, 42, 46,

47, 49, 50, 53, 54, 56, 63, 64, 65, 68, 69,

70, 74–79, 80, 81, 84, 87, 88, 99, 111, 113,

114, 115, 116, 117, 118, 119, 120, 122,

123, 124, 125, 126, 127, 128, 131, 134,

135, 137, 138, 139, 140, 146, 155, 162,

175, 176, 193, 194, 195, 198, 208, 209,

210, 215, 220, 221

Motional diamagnetism, 188

Moving pairon, 12, 73, 75, 77–79, 89, 90, 92,

95, 96, 136, 137, 138, 139, 167, 170, 178,

212, 221, 222

uller, 9, 157, 197, 215

−xCexCuO

, 173, 174, 175, 177, 178, 183,

190, 197, 199, 205

Neck-like hyperboloidal Fermi surface, 42

eel temperature, 173, 174, 182, 205

Negative energy, 77, 91

Negative-energy state, 91

Index 247

Negative ion, 161, 175

Negative resistance region, 97, 99, 101

Net momentum, 24, 26, 53, 63, 64, 65, 75, 76,

77, 80, 135, 198

Never-decaying supercurrent, 1, 3

Nonmagnetic impurity, 223

Normal coordinate, 16

Normal current, 6, 12, 114, 121, 126, 146,

150, 154

Normal metal, 43, 170

Normal-mode frequency, 16, 17

n-type, 173

Nuclear force, 161, 209

Number operator, 30, 52, 62, 63, 65, 69, 74,

79, 124, 227

Number of phonons, 17

Occupation number, 56, 62, 64, 67, 227, 233

Ochsenfeld, 1, 207

O-Fermi surface, 174, 176, 177, 195, 204, 205

Ohm’s law, 91, 92, 96, 100, 150, 154, 200, 201

One-body density matrix, 48

One-body density operator, 48

One-body quantum Liouville equation, 125

One-body trace, 46, 134

Onsager’s formula, 159

Onsager’s quantum ﬂux, 188

Onsager’s solution, 215

Optical phonon, 88, 108–110, 111, 157, 161,

162, 173, 174, 175, 178, 193, 195, 196,

221, 222

Optical phonon exchange, 157, 161, 173, 174,

175, 193, 195, 196

Order of phase transition, 83

Pair-annihilation operator, 37, 111, 125

Pair creation, 33, 34, 37, 56, 67, 97, 111, 125,

162, 165, 175, 176, 195, 210

Pairing interaction Hamiltonian, 210

Pairon, 10, 11, 12, 29, 30, 31, 32, 33, 34,

37, 39, 40, 41–42, 43, 45, 49, 53, 54, 55,

56, 59–65, 69, 73, 75, 77–79, 86, 88, 89,

91–101, 108, 111, 113, 114, 115, 116, 120,

121, 125, 127, 128, 131–140, 143, 146,

147, 148, 150, 152, 153–154, 155, 157,

160, 162, 165, 167, 169, 170, 175, 177,

178, 181, 187, 189, 194, 195–196, 198,

201, 203, 208, 210, 211, 212, 213, 215,

219–224

Pairon energy, 55, 89, 92, 95, 97, 98, 101, 131,

133, 136, 137, 140, 169, 170, 209, 212, 221

Pairon energy gap, 89, 97, 101, 131, 133, 136,

137, 140, 169, 170, 209, 221

Pairon with zero net momentum, 75

Pair wavefunction, 77

Parent material, 173, 175, 182, 205

Pauli, 12, 42, 64, 68, 69, 70, 183, 184, 187, 227

Pauli exclusion principle, 64

Pauli paramagnetism, 184

Penetration depth, 3, 105, 106, 111, 113,

119–123, 128, 131, 133, 138–140, 208,

220, 222, 223

Perfect-diamagnetic, 3

Permutation symmetry, 68, 69, 234

Perovskite structure, 182, 183, 190, 205

Phase change, 1, 6–7, 13, 73, 157, 205,

219, 221

Phase diagram, 9, 107, 174, 183, 199, 205

Phase difference, 116, 117, 119, 120, 122, 128,

148, 149, 150, 214

Phonon, 10, 11, 12, 15–27, 29, 30, 31, 32, 37,

41, 42, 50, 56, 71, 77, 88, 103, 108–110,

114, 125, 137, 161, 162, 163, 168, 174,

176, 178, 188, 193–195, 198, 200, 201,

205, 209–210, 212, 219, 221, 222, 223

Phonon exchange attraction, 10, 12, 23–27, 30,

77, 137, 163, 174, 193–195, 205, 219

Phonon scattering, 15, 201

Photon, 68, 70, 71, 93, 96, 97, 146, 147,

155, 219

Physical vacuum state, 31, 34, 37, 165

pi (π) meson, 111

Planck distribution, 17, 93, 95, 99

Planck distribution function, 17, 93, 95, 99

Point contact, 144, 145

Point-like repulsion, 131, 133, 135, 140

Positive ion, 175

Principal-axis transformation, 16

p-type, 173

Quantum Hall effect (QHE), 215–216, 227

Quantum Liouville equation, 25, 47, 124, 125,

154, 193

Quantum Liouville operator, 25

Quantum nonlinear equation, 136

Quantum statistical factor, 95, 99, 146

Quantum statistical postulate, 61

Quantum statistical theory, 1, 12–13, 25,

73–88, 225

Quantum Theory of Conducting Matter, 216

Quantum transition rate, 94

Quantum tunneling, 6, 39, 89–101, 133, 136,

143, 168–170, 212, 213, 221

248 Index

Quasi-electron, 11, 12, 29, 36, 40, 41, 45, 49,

51, 55, 56, 57, 59, 60, 89, 90, 91, 96, 137,

168, 207, 211, 212, 213, 221, 222

Quasi-electron energy, 11, 45, 137, 168,

211, 212

Quasi-electron energy gap, 11, 137, 168,

211, 212

Quasi-wavefunction, 47, 113, 116–118,

123–126, 143, 148, 152, 153–154

Reduced Hamiltonian, 30–32, 39, 40, 41, 49,

50, 54, 124, 125, 163

Relative momentum, 10, 36, 52, 63, 74, 75, 89,

90, 94, 95, 96, 105, 123, 159, 189, 190,

202, 212

Resonating valence bond, 215

Revised London equation, 128, 208

Ring-shaped cylindrical superconductor, 3

Ring supercurrent, 3–4, 73, 113–116, 117, 118,

134, 153, 154

Schr

odinger equation, 126, 154, 236

Second quantization formulation, 10, 209, 235

Self-focusing power, 146, 147, 153, 214, 220

Sharp Fermi surface, 10, 30, 43

Sharp phase change, 1, 6–7, 13, 219

Shockley’s formula, 159

Short-ranged nuclear force, 161

Shoulder, 168

Silsbee’s rule, 223–224

Simple cubic lattice, 108

Single-particle state, 234, 236

Small pocket, 161, 162, 175, 176, 195

Spin-statistics theorem, 68, 69, 70

Stationary, 41, 47, 49, 51, 54, 55, 75, 76,

77, 89, 90, 106, 125, 126, 138, 140, 163,

212, 220

Stephan-Boltzmann law, 85

Supercondensate, 11, 12, 37, 41, 42–43, 45,

49, 50, 51, 54, 56, 57, 58, 59, 60, 90, 92,

95, 96, 99, 101, 103, 106, 108, 111, 113,

115, 116, 124, 125, 126, 128, 132, 134,

136, 137, 147, 150, 151, 152, 153, 154,

160, 162, 165, 175, 207, 208, 215, 219,

220, 221, 223

Superconducting quantum interference device

(SQUID), 5, 116, 143, 149, 153, 214

Superconducting state, 8, 9, 12, 39, 41, 87, 88,

89, 103, 104, 105, 106, 111, 127, 128, 157,

169, 174, 177, 205, 212, 220, 221, 222

Superconductor, 1–13, 29, 30, 37, 39, 41, 42,

43, 45, 57, 87, 90, 91, 92, 94, 97, 99, 100,

103–111, 113, 114, 115, 116, 119, 121,

127, 131, 132, 136, 138, 143, 144, 147,

148, 153, 154, 157–171, 181, 189, 197,

204, 207, 208, 209, 212, 213, 214, 215,

219, 220, 221, 222, 223, 224

Supercurrent, 1, 3–4, 5, 6, 9, 12, 13, 32, 41, 73,

91, 92, 103, 104, 105, 106, 113–129, 132,

134, 138, 139, 143, 144, 145, 146, 147,

149, 150, 151, 152, 153, 154, 155, 160,

208, 209, 211, 214, 215, 220, 221, 222,

223, 224

Supercurrent interference, 146, 155

Supercurrent tunneling, 143, 144, 214

Superelectron, 119, 128, 132, 135, 139, 140,

147, 209

Superelectron model, 132, 135, 139, 140, 147

Super-to-normal transition, 181

Susceptibility, 178, 181–191

Symmetric state, 65, 69

Thermodynamic critical ﬁeld, 107, 115,

167, 224

Thin ﬁlm, 8, 90, 159, 222

Third-order phase transition, 83, 85

Threshold voltage, 90, 91, 92, 96, 99, 100,

170, 221

T-linear behavior, 197

Torque magnetometry, 159

Total pair number, 79

T-quadratic behavior, 197, 203, 205

Transverse acoustic, 110

Transverse optical, 110

Transverse wave, 19

Tunneling junction, 144, 145

Two energy gaps, 36, 89, 97, 100, 157,

168–170, 222

Two-ﬂuid model, 207

Two-particle composite, 62–68

Type II magnetic behavior, 8, 13, 103, 157

Type II superconductor, 9, 103–108, 111, 132,

209, 224

Type I superconductor, 8, 103, 107, 111, 136,

161, 166, 170, 224

Unpaired electron, 11, 36, 40, 45, 51, 56,

59, 137

Upper critical ﬁeld, 8, 9, 103, 104, 138, 224

Up-spin, 51, 185, 186

Vacuum ket, 21, 229, 230

van Hove, 18

Index 249

van Hove singularity, 18

Voltage standard, 154

Vortex, 103, 104, 105, 106, 108, 132, 138, 207,

209, 224

Vortex structure, 104, 105, 132,

138, 209

Wave function, 35, 46, 47, 48, 59, 76,

77, 235

Wavelength, 18, 19, 147, 154, 161, 195

Weak-coupling approximation, 26

Weak link, 144, 145

YBa

, 157, 158

Yukawa, 111, 209

Zero-momentum boson, 80, 84

Zero-momentum pairon, 31, 39, 79

Zero resistance, 1, 4, 6, 13, 103, 157, 219, 223

Fujita S., Ito K., Godoy S. Quantum Theory of Conducting Matter - Superconductivity

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