6.3.2 many-body states in single-mode approximation
6.3.3 superflow, spin texture, and berry phase
6.4 spin-2 bec
7. 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 bec 
8. 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 states
9. 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-linigermodel
10. dipolar gases 
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 interaction 
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 circulation
11. optical lattices 
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 supersolid
12. 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 charges
appendix a order of phase transition, clausius-clapeyron
formula, and gibbs-duhem relation 
appendix b bogoliubov wave functions in coordinate space 
b.1 ground-state wave function.
b.2 one-phonon state
appendix c effective mass, sound velocity, and spin
susceptibility of fermi liquid 
appendix d derivation of eq. (8.155) 
appendix e f -sum rule 
bibliography 
index

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