| Preface |
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ix | |
| Abbreviations |
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xii | |
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1 Introduction to Superconductivity |
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1 | (44) |
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1.1 Basic Properties of Superconductivity |
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1 | (2) |
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1.2 Two-Fluid Model and London Equations |
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3 | (3) |
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6 | (2) |
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1.4 BCS Mean Field Theory |
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8 | (5) |
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1.5 Bogoliubov-de Gennes Self-consistent Equation |
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13 | (1) |
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1.6 Charge and Probability Current Density Operators |
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14 | (3) |
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1.7 Off-Diagonal Long-Range Order |
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17 | (2) |
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1.8 Ginzburg-Landau Free Energy |
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19 | (4) |
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23 | (1) |
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1.10 Two Types of Superconductor |
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24 | (4) |
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1.11 Spontaneous Symmetry Breaking and Meissner Effect |
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28 | (1) |
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1.12 Two Characteristic Energy Scales |
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29 | (3) |
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32 | (1) |
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1.14 Classification of Pairing Symmetry |
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33 | (4) |
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1.15 Pairing Symmetry of Cuprate Superconductors |
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37 | (4) |
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1.16 Pairing Symmetry of Iron-Based Superconductors |
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41 | (4) |
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2 Microscopic Models for High Temperature Superconductors |
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45 | (27) |
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2.1 Phase Diagram of Cuprate Superconductors |
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45 | (4) |
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2.2 Antiferromagnetic Insulating States |
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49 | (2) |
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51 | (2) |
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2.4 DP Model of Interacting Spins and Holes |
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53 | (3) |
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56 | (1) |
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57 | (3) |
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2.7 Interlayer Electronic Structures |
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60 | (2) |
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2.8 Systems with Zn or Ni Impurities |
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62 | (10) |
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3 Basic Properties of d-wave Superconductors |
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72 | (21) |
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72 | (2) |
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3.2 Temperature Dependence of the d-Wave Energy Gap |
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74 | (5) |
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79 | (2) |
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81 | (3) |
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84 | (3) |
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3.6 Gap Operators in the Continuum Limit |
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87 | (4) |
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91 | (2) |
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4 Quasiparticle Excitation Spectra |
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93 | (17) |
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4.1 Single-Particle Spectral Function |
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93 | (2) |
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95 | (6) |
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4.3 Fermi Surface and Luttinger Sum Rule |
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101 | (2) |
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4.4 Particle--Hole Mixing and Superconducting Energy Gap |
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103 | (4) |
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4.5 Scattering Between Quasiparticles |
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107 | (3) |
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110 | (29) |
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110 | (5) |
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5.2 Tunneling Conductance |
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115 | (2) |
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5.3 Scattering from the δ-Function Interface Potential |
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117 | (7) |
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124 | (2) |
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5.5 Tunneling Hamiltonian |
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126 | (4) |
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130 | (3) |
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5.7 Tunneling Effect of Quasiparticles |
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133 | (6) |
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139 | (19) |
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6.1 Josephson Tunneling Current |
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139 | (4) |
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6.2 Spontaneous Magnetic Flux Quantization |
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143 | (2) |
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6.3 Phase-Sensitive Experiments |
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145 | (9) |
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6.4 Paramagnetic Meissner Effect |
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154 | (4) |
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7 Single Impurity Scattering |
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158 | (26) |
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7.1 Nonmagnetic Impurity Scattering |
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158 | (7) |
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165 | (2) |
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7.3 Correction to the Density of States |
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167 | (4) |
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7.4 Tunneling Spectrum of Zinc Impurity |
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171 | (2) |
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7.5 Comparison with Anisotropic 5-Wave Pairing State |
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173 | (2) |
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7.6 Classical Spin Scattering |
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175 | (3) |
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178 | (1) |
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7.8 Quasiparticle Interference |
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179 | (5) |
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8 Many-Impurity Scattering |
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184 | (20) |
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8.1 Scattering Potential and Disorder Average |
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184 | (2) |
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186 | (4) |
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8.3 Born Scattering Limit |
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190 | (3) |
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8.4 Resonant Scattering Limit |
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193 | (3) |
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8.5 Correction to the Superconducting Critical Temperature |
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196 | (3) |
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199 | (3) |
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8.7 Entropy and Specific Heat |
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202 | (2) |
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204 | (36) |
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9.1 Linear Response Theory of Superfluids |
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204 | (4) |
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208 | (2) |
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9.3 Superfluid Response in Cuprate Superconductors |
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210 | (8) |
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218 | (4) |
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9.5 Superfluid Response in a Weakly Coupled Two-Band Superconductor |
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222 | (4) |
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9.6 Electron-Doped Cuprate Superconductors |
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226 | (3) |
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229 | (6) |
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9.8 Non-linear Correction to the Penetration Depth |
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235 | (1) |
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236 | (4) |
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10 Optical and Thermal Conductivities |
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240 | (28) |
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10.1 Optical Conductivity |
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240 | (2) |
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242 | (3) |
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10.3 Light Absorption in the Dirty Limit |
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245 | (6) |
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10.4 Effect of Elastic Impurity Scattering |
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251 | (4) |
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10.5 Microwave Conductivity of Cuprate Superconductors |
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255 | (5) |
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10.6 Heat Current Density Operator |
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260 | (3) |
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10.7 Universal Thermal Conductivity |
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263 | (5) |
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268 | (16) |
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11.1 Raman Response Function |
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268 | (3) |
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271 | (2) |
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11.3 Vertex Correction by the Coulomb Interaction |
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273 | (2) |
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11.4 Raman Response in a Superconducting State |
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275 | (3) |
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11.5 Effect of Nonmagnetic Impurity Scattering |
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278 | (1) |
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11.6 Experimental Results of Cuprate Superconductors |
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279 | (5) |
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12 Nuclear Magnetic Resonance |
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284 | (22) |
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12.1 Spin Correlation Function |
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284 | (2) |
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12.2 Hyperfine Interaction |
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286 | (3) |
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289 | (1) |
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12.4 Spin-Lattice Relaxation |
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290 | (7) |
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12.5 Effect of Impurity Scattering |
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297 | (1) |
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12.6 Impurity Resonance States |
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298 | (5) |
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12.7 Experimental Results of Cuprate Superconductors |
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303 | (3) |
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13 Neutron Scattering Spectroscopy |
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306 | (18) |
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13.1 Neutron Scattering and Magnetic Susceptibility |
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306 | (3) |
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13.2 Magnetic Resonances in High-Tc Superconductors |
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309 | (4) |
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13.3 Implications of the Magnetic Resonances |
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313 | (1) |
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13.4 Origin of the Magnetic Resonance |
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314 | (10) |
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324 | (19) |
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14.1 Caroli--de Gennes--Matricon Vortex Core State |
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324 | (7) |
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14.2 Semiclassical Approximation |
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331 | (4) |
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14.3 Low-Energy Density of States |
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335 | (4) |
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14.4 Universal Scaling Laws |
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339 | (4) |
| Appendix A Bogoliubov Transformation |
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343 | (3) |
| Appendix B Hohenberg Theorem |
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346 | (6) |
| Appendix C Degenerate Perturbation Theory |
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352 | (2) |
| Appendix D Anderson Theorem |
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354 | (2) |
| Appendix E Sommerfeld Expansion |
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356 | (2) |
| Appendix F Single-Particle Green's Function |
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358 | (5) |
| Appendix G Linear Response Theory |
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363 | (3) |
| References |
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366 | (18) |
| Index |
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384 | |