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1 Quantum liquids 11 Indistinguishability and the symmetry of the many-body wave function 3 1.2 The ermni-Dirac and BoseEinstein disributions: BEC in a noninteracting gas 8 1.3 Cooper pairing 13 I:4 The experimental systems 15 S.5 Superconductivity and superfluidty basic phenomenology 20 Appendix 26 S EC: Its definition, origin, occurrence, and consequences 31 2.1 Definition of BEC in an interacting system 31 2.2 The order parameter and the superfluid velocity; alternative definitions of BEC 34 2.3 Why should BEC occur in an interacting system? When does it (not)? 40 2 Pseudo-BEC in a Fermi system (Cooper pairing) 46 2.5 The consequences of BEG: preview of coming attractions 53 2.6 Fragmented BEC 60 Appendices 63 3 Liquid He 71 3.1 Anomalous properties of the He-HI phase 72 312 Direct evidence for BEC in He-1 73 33 The two-fluid model of He-II: static effects 76 3.4 The two-fluid model: dynaical effects 83 3.5 Quantized vortices, phase slip and the Josephson effect 9 S3. The excitation spectrum of liquid He-II 98 3.7 Microscopic theories of He-II 02 4 The Bose alkali gases 13 4.1 The atoms: structure, trapping, and diagnostics 113 42 s-wave scattering and effective interaction 11 4.3 The Gross-Pitaevskii equation: some simple applications 123 4.4 The Bogoliubov approximation 1.31 45 Coherence and interference in dilute alkali Bose gases 134 4.6 Optical lattices 145 S7 Signatnures of superfluidity in the BEC alkali gases 50 Appen ix 157 5 Classical superconductivity 165 5.1 The normal state 165 5.2 The effective electron-electron interaction 170 5.3 The Cooper instability 175 5.4 BCS theory at 7 0 178 5.5 Excited states and finite-temperature BCS theory 18 5.6 The two-fluid model fr superconductors: the Meissne effect 190 5.7 The Ginzburg-Landau theory 198 5.8 Generalizations of BCS: the "non-pair-breaking case 208 5.9 Pair-breaking effects 216 5.10 The Josephson effe t 223 Appendices 228 6 Superfluid 3He 251 6.1 The normal phase of liquid 3He 251 6.2 Anisotropic Cooper pairing 254 6.3 Generalized Ginzburg-Landau approach: spin fluctuation feedback 260 6.4 Spontaneously broken spin-orbit synmetry and spin dynamics 265 6.5 Supercurrents, textures and defects 272 Appendix 281 7 Cuprate superconductivity 283 "71 Introduction 283 7.2 The cuprates: composition, structure, and phase diagram 284 .3 The cuprates: principal experimental properties 295 7.4 Normal state at optimal doping 296 .5 The "pseudogap" regime 302 7.6 Superconducting state 304 .7 Some preliminary comments on the experimental data 313 7.8 What do we know for sure about cuprate superconductivity? 314 7.9 The cuprates: questions and ideas 326 .10 Novel consequences of Cooper pairing in the cuprates 336 Appendices 34 8 Miscellaneous topics 349 8.1 Noncuprate exotic" superconductors 349 82 Liquid SHe in aerogel 355 8.3 Supersolids 358 8.4 Fermi alkali gases: the BEC-BCS crossover 64 Appendix 371

Library of Congress subject headings for this publication: Superconductivity, Quantum liquids, Condensation