玻色-爱因斯坦凝聚的基础与前沿=FUNDAMENTALS AND NEW FRONTIERS OF BOSE-EINSTEIN CONDENSATION 英文 影印版PDF|Epub|txt|kindle电子书版本下载

玻色-爱因斯坦凝聚的基础与前沿=FUNDAMENTALS AND NEW FRONTIERS OF BOSE-EINSTEIN CONDENSATION 英文 影印版PDF格式电子书版下载

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1．Fundamentals of Bose-Einstein Condensation1

1.1 Indistinguishability of Identical Particles1

1.2 Ideal Bose Gas in a Uniform System3

1.3 Off-Diagonal Long-Range Order：Bose System6

1.4 Off-Diagonal Long-Range Order：Fermi System10

1.5 U（1）Gauge Symmetry11

1.6 Ground-State Wave Function of a Bose System13

1.7 BEC and Superfluidity15

1.8 Two-Fluid Model20

1.9 Fragmented Condensate23

1.9.1 Two-state model23

1.9.2 Degenerate double-well model25

1.9.3 Spin-1 antiferromagnetic BEC27

1.10 Interference Between Independent Condensates28

1.11 Feshbach Resonance31

2．Weakly Interacting Bose Gas33

2.1 Interactions Between Neutral Atoms33

2.2 Pseudo-Potential Method36

2.3 Bogoliubov Theory40

2.3.1 Bogoliubov transformations40

2.3.2 Bogoliubov ground state45

2.3.3 Low-lying excitations and condensate fraction48

2.3.4 Properties of Bogoliubov ground state50

2.4 Bogoliubov Theory of Quasi-One-Dimensional Torus54

2.4.1 Case of BEC at rest：stability of BEC55

2.4.2 Case of rotating BEC：Landau criterion56

2.4.3 Ground state of BEC in rotating torus59

2.5 Bogoliubov-de Gennes（BdG）Theory60

2.6 Method of Binary Collision Expansion65

2.6.1 Equation of state65

2.6.2 Cluster expansion ofpartition function66

2.6.3 Ideal Bose and Fermi gases67

2.6.4 Matsubara formula69

3．Trapped Systems73

3.1 Ideal Bose Gas in a Harmonic Potential73

3.1.1 Transition temperature75

3.1.2 Condensate fraction76

3.1.3 Chemical potential77

3.1.4 Specific heat77

3.2 BEC in One-and Two-Dimensional Parabolic Potentials79

3.2.1 Density of states79

3.2.2 Transition temperature79

3.2.3 Condensate fraction80

3.3 Semiclassical Distribution Function81

3.4 Gross-Pitaevskii Equation83

3.5 Thomas-Fermi Approximation84

3.6 Collective Modes in the Thomas-Fermi Regime88

3.6.1 Isotropic harmonic potential89

3.6.2 Axisymmetric trap91

3.6.3 Scissors mode92

3.7 Variational Method93

3.7.1 Gaussian variational wave function94

3.7.2 Collective modes96

3.8 Attractive Bose-Einstein Condensate98

3.8.1 Collective modes99

3.8.2 Collapsing dynamics of an attractive condensate102

4．Linear Response and Sum Rules105

4.1 Linear Response Theory105

4.1.1 Linear response of density fluctuations105

4.1.2 Retarded response function108

4.2 Sum Rules109

4.2.1 Longitudinal f-sum rule110

4.2.2 Compressibility sum rule112

4.2.3 Zero energy gap theorem114

4.2.4 Josephson sum rule115

4.3 Sum-Rule Approach to Collective Modes120

4.3.1 Excitation operators121

4.3.2 Virial theorem122

4.3.3 Kohn theorem123

4.3.4 Isotropic trap124

4.3.5 Axisymmetric trap127

5．Statistical Mechanics of Superfluid Systems in a Moving Frame129

5.1 Transformation to Moving Frames129

5.2 Elementary Excitations of a Superfluid131

5.3 Landau Criterion133

5.4 Correlation Functions at Thermal Equilibrium134

5.5 Normal Fluid Density136

5.6 Low-Lying Excitations of a Superfluid140

5.7 Examples141

5.7.1 Ideal Bose gas141

5.7.2 Weakly interacting Bose gas143

6．Spinor Bose-Einstein Condensate145

6.1 Internal Degrees of Freedom145

6.2 General Hamiltonian of Spinor Condensates146

6.3 Spin-1 BEC151

6.3.1 Mean-field theory of a spin-1 BEC153

6.3.2 Many-body states in single-mode approximation157

6.3.3 Superflow,spin texture,and Berry phase161

6.4 Spin-2 BEC163

7．Vortices171

7.1 Hydrodynamic Theory of Vortices171

7.2 Quantized Vortices174

7.3 Interaction Between Vortices180

7.4 Vortex Lattice181

7.4.1 Dynamics of vortex nucleation181

7.4.2 Collective modes of a vortex lattice183

7.5 Fractional Vortices186

7.6 Spin Current187

7.7 Fast Rotating BECs189

7.7.1 Lowest Landau level approximation189

7.7.2 Mean field quantum Hall regime192

7.7.3 Many-body wave funetions of a fast rotating BEC194

8．Fermionic Superfluidity197

8.1 Ideal Fermi Gas197

8.2 Fermi Liquid Theory200

8.3 Cooper Problem205

8.3.1 Two-body problem205

8.3.2 Many-body problem209

8.4 Bardeen-Cooper-Schriefier (BCS) Theory211

8.5 BCS-BEC Crossover at T=0215

8.6 Superfluid Transition Temperature219

8.7 BCS-BEC Crossover at T≠0221

8.8 Gor'kov-Melik-Barkhudarov Correction225

8.9 Unitary Gas228

8.10 Imbalanced Fermi Systems231

8.11 P-Wave Superfluid234

8.11.1 Generalized pairing theory234

8.11.2 Spin-triplet p-wave states238

9．Low-Dimensional Systems241

9.1 Non-interacting Systems241

9.2 Hohenberg-Mermin-Wagner Theorem243

9.3 Two-Dimensional BEC at Absolute Zero246

9.4 Berezinskii-Kosterlitz-Thouless Transition247

9.4.1 Universal jump247

9.4.2 Quasi long-range order249

9.4.3 Renormalization-group analysis250

9.5 Quasi One-Dimensional BEC252

9.6 Tonks-Girardeau Gas256

9.7 Lieb-Liniger Model258

10．Dipolar Gases261

10.1 Dipole-Dipole Interaction261

10.1.1 Basic properties261

10.1.2 Order of magnitude and length scale263

10.1.3 D-wave nature264

10.1.4 Tuning the dipole-dipole interaction265

10.2 Polarized Dipolar BEC266

10.2.1 Nonlocal Gross-Pitaevskii equation266

10.2.2 Stability267

10.2.3 Thomas-Fermi limit269

10.2.4 Quasi two-dimensional systems271

10.3 Spinor-Dipolar BEC273

10.3.1 Einstein-de Haas effect274

10.3.2 Flux closure and ground-state circulation274

11．Optical Lattices277

11.1 Optical Potential277

11.1.1 Optical trap277

11.1.2 Optical lattice280

11.2 Band Structure283

11.2.1 Bloch theorem283

11.2.2 Brillouin zone285

11.2.3 Bloch oscillations286

11.2.4 Wannier function287

11.3 Bose-Hubbard Model288

11.3.1 Bose-Hubbard Hamiltonian288

11.3.2 Superfluid-Mott-insulator transition289

11.3.3 Phase diagram291

11.3.4 Mean-field approximation292

11.3.5 Supersolid295

12．Topological Excitations297

12.1 Homotopy Theory297

12.1.1 Homotopic relation297

12.1.2 Fundamental group299

12.1.3 Higher homotopy groups302

12.2 Order Parameter ManifoId303

12.2.1 Isotropy group303

12.2.2 Spin-1 BEC304

12.2.3 Spin-2 BEC305

12.3 Classification of Defects306

12.3.1 Domains306

12.3.2 Line defects306

12.3.3 Point defects311

12.3.4 Skyrmions313

12.3.5 Influence of different types of defects316

12.3.6 Topological charges318

Appendix A Order of Phase Transition，Clausius-Clapeyron Formula,and Gibbs-Duhem Relation321

Appendix B Bogoliubov Wave Functions in Coordinate Space323

B.1 Ground-State Wave Function323

B.2 One-Phonon State327

Appendix C Effective Mass，Sound Velocity,and Spin Susceptibility of Fermi Liquid329

Appendix D Derivation of Eq.（8.155）333

Appendix E f-Sum Rule335

Bibliography337

Index347