首先介紹了玻色-愛因斯坦凝聚（BEC）的基本理論。之后，本書討論了快速旋轉BEC，旋量和偶極BEC，低維BEC等近來發展迅速的方向。本書還介紹了平衡或非平衡費米液體超流，包括BCS-BEC交叉、幺正氣體、p波超流等。本書適合本領域的研究者和研究生閱讀。

Preface v1. Fundamentals of Bose-Einstein Condensation 1.1 Indistinguishability of Identical Particles 1.2 Ideal Bose Gas in a Uniform System 1.3 Off-Diagonal Long-Range Order: Bose System 1.4 Off-Diagonal Long-Range Order: Fermi System 1.5 U(1)Gauge Symmetry 1.6 Ground-State Wave Function of a Bose System 1.7 BEC and Superfluidity 1.8 Two-FluidModel 1.9 Fragmented Condensate 1.9.1 Two-statemodel 1.9.2 Degenerate double-well model 1.9.3 Spin-1 antiferromagic BEC 1.10 Interference Between Independent Condensates 1.11 Feshbach Resonance2. Weakly Interacting Bose Gas 2.1 Interactions Between Neutral Atoms 2.2 Pseudo-PotentialMethod 2.3 Bogoliubov Theory 2.3.1 Bogoliubov transformations 2.3.2 Bogoliubov ground state 2.3.3 Low-lying excitations and condensate fraction 2.3.4 Properties of Bogoliubov ground state 2.4 Bogoliubov Theory of Quasi-One-Dimensional Torus 2.4.1 Case of BEC at rest: stability of BEC 2.4.2 Case of rotating BEC: Landau criterion 2.4.3 Ground state of BEC in rotating torus 2.5 Bogoliubov-deGennes (BdG) Theory 2.6 Method of Binary Collision Expansion 2.6.1 Equation of state 2.6.2 Cluster expansion of partition function 2.6.3 Ideal Bose and Fermi gases 2.6.4 Matsubara formula3. Trapped Systems 73 3.1 Ideal Bose Gas in a Harmonic Potential 3.1.1 Transition temperature 3.1.2 Condensate fraction 3.1.3 Chemical potential 3.1.4 Specific heat 3.2 BEC in One- and Two-Dimensional Parabolic Potentials 3.2.1 Density of states 3.2.2 Transition temperature 3.2.3 Condensate fraction 3.3 Semiclassical Distribution Function 3.4 Gross-Pitaevskii Equation 3.5 Thomas-Fermi Approximation 3.6 Collective Modes in the Thomas-Fermi Regime 3.6.1 Isotropic harmonic potential 3.6.2 Axisymmetric trap 3.6.3 Scissorsmode 3.7 VariationalMethod 3.7.1 Gaussian variational wave function 3.7.2 Collectivemodes 3.8 Attractive Bose-Einstein Condensate 3.8.1 Collectivemodes 3.8.2 Collapsing dynamics of an attractive condensate4. Linear Response and Sum Rules 4.1 Linear Response Theory 4.1.1 Linear response of density fluctuations 4.1.2 Retarded response function 4.2 Sum Rules 4.2.1 Longitudinal f-sumrule 4.2.2 Compressibility sum rule 4.2.3 Zero energy gap theorem 4.2.4 Josephson sum rule 4.3 Sum-Rule Approach to CollectiveModes 4.3.1 Excitation operators 4.3.2 Virial theorem 4.3.3 Kohn theorem 4.3.4 Isotropic trap 4.3.5 Axisymmetric trap5. Statistical Mechanics of Superfluid Systems in a Moving Frame 5.1 Transformation toMoving Frames 5.2 Elementary Excitations of a Superfluid 5.3 Landau Criterion 5.4 Correlation Functions at Thermal Equilibrium 5.5 Normal Fluid Density 5.6 Low-Lying Excitations of a Superfluid 5.7 Examples 5.7.1 Ideal Bose gas 5.7.2 Weakly interacting Bose gas6. Spinor Bose-Einstein Condensate 6.1 Internal Degrees of Freedom 6.2 General Hamiltonian of Spinor Condensates 6.3 Spin-1 BEC 6.3.1 Mean-field theory of a spin-1 BEC 6.3.2 Many-body states in single-mode approximation 6.3.3 Superflow, spin texture, and Berry phase 6.4 Spin-2 BEC7. Vortices 7.1 Hydrodynamic Theory of Vortices 7.2 Quantized Vortices 7.3 Interaction Between Vortices 7.4 Vortex Lattice 7.4.1 Dynamics of vortex nucleation 7.4.2 Collective modes of a vortex lattice 7.5 FractionalVortices 7.6 Spin Current 7.7 Fast Rotating BECs 7.7.1 Lowest Landau level approximation 7.7.2 Mean field quantum Hall regime 7.7.3 Many-body wave functions of a fast rotating BEC8. Fermionic Superfluidity 8.1 Ideal Fermi Gas 8.2 Fermi Liquid Theory 8.3 Cooper Problem 8.3.1 Two-body problem 8.3.2 Many-body problem 8.4 Bardeen-Cooper-Schrieffer (BCS) Theory 8.5 BCS-BEC Crossover at T＝0 8.6 Superfluid Transition Temperature 8.7 BCS-BEC Crossover at T≠0 8.8 Gor’’kov-Melik-Barkhudarov Correction 8.9 Unitary Gas 8.10 Imbalanced Fermi Systems 8.11 P-Wave Superfluid 8.11.1 Generalized pairing theory 8.11.2 Spin-triplet p-wave states9. Low-Dimensional Systems 9.1 Non-interacting Systems 9.2 Hohenberg-Mermin-Wagner Theorem 9.3 Two-Dimensional BEC at Absolute Zero 9.4 Berezinskii-Kosterlitz-Thouless Transition 9.4.1 Universal jump 9.4.2 Quasi long-range order 9.4.3 Renormalization-group analysis 9.5 Quasi One-Dimensional BEC 9.6 Tonks-Girardeau Gas 9.7 Lieb-LinigerModel10. Dipolar Gases 261 10.1 Dipole-Dipole Interaction 10.1.1 Basic properties 10.1.2 Order of magnitude and length scale 10.1.3 D-wave nature 10.1.4 Tuning the dipole-dipole interaon 10.2 PolarizedDipolar BEC 10.2.1 Nonlocal Gross-Pitaevskii equation 10.2.2 Stability 10.2.3 Thomas-Fermi limit 10.2.4 Quasi two-dimensional systems 10.3 Spinor-Dipolar BEC 10.3.1 Einstein-de Haas effect 10.3.2 Flux closure and ground-state circulation11. Optical Lattices 277 11.1 Optical Potential 11.1.1 Optical trap 11.1.2 Optical lattice 11.2 Band Structure 11.2.1 Bloch theorem 11.2.2 Brillouin zone 11.2.3 Bloch oscillations 11.2.4 Wannier function 11.3 Bose-Hubbard Model 11.3.1 Bose-Hubbard Hamiltonian 11.3.2 Superfluid-Mott-insulator transition 11.3.3 Phase diagram 11.3.4 Mean-field approximation 11.3.5 Supersolid12. Topological Excitations 12.1 Homotopy Theory 12.1.1 Homotopic relation 12.1.2 Fundamental group 12.1.3 Higher homotopy groups 12.2 Order Parameter Manifold 12.2.1 Isotropy group 12.2.2 Spin-1 BEC 12.2.3 Spin-2 BEC 12.3 Classification of Defects 12.3.1 Domains 12.3.2 Line defects 12.3.3 Point defects 12.3.4 Skyrmions 12.3.5 Influence of different types of defects 12.3.6 Topological chargesAppendix A Order of Phase Transition, Clausius-Clapeyron Formula, and Gibbs-Duhem RelationAppendix B Bogoliubov Wave Functions in Coordinate Space B.1 Ground-State Wave Function B.2 One-Phonon StateAppendix C Effective Mass, Sound Velocity, and Spin Susceptibility of Fermi LiquidAppendix D Derivation of Eq. (8.155)Appendix E f -Sum RuleBibliographyIndex