有限温度玻色凝聚气体

Preface page ix

1 Overview and introduction 1

1.1 Historical overview of Bose superfluids 9

1.2 Summary of chapters 12

2 Condensate dynamics at T = 0 19

2.1 Gross-Pitaevskii (GP) equation 20

2.2 Bogoliubov equations for condensate fluctuations 28

3 Coupled equations for the condensate

and thermal cloud 32

3.1 Generalized GP equation for the condensate 33

3.2 Boltzmann equation for the noncondensate atoms 39

3.3 Solutions in thermal equilibrium 43

3.4 Region of validity of the ZNG equations 46

4 Green's functions and self-energy approximations 54

4.1 Overview of Green's function approach 54

Preface page ix

1 Overview and introduction 1

1.1 Historical overview of Bose superfluids 9

1.2 Summary of chapters 12

2 Condensate dynamics at T = 0 19

2.1 Gross-Pitaevskii (GP) equation 20

2.2 Bogoliubov equations for condensate fluctuations 28

3 Coupled equations for the condensate

and thermal cloud 32

3.1 Generalized GP equation for the condensate 33

3.2 Boltzmann equation for the noncondensate atoms 39

3.3 Solutions in thermal equilibrium 43

3.4 Region of validity of the ZNG equations 46

4 Green's functions and self-energy approximations 54

4.1 Overview of Green's function approach 54

4.2 Nonequilibrium Green's functions in normal systems 58

4.3 Green's functions in a Bose-condensed gas 68

4.4 Classification of self-energy approximations 74

4.5 Dielectric formalism 79

5 The Beliaev and the time-dependent HFB

approximations 81

5.1 Hartree-Fock-Bogoliubov self-energies 82

5.2 Beliaev self-energy approximation 87

5.3 Beliaev as time-dependent HFB 92

5.4 Density response in the Beliaev-Popov approximation 98

6 Kadanoff-Baym derivation of the ZNG equations 107

6.1 Kadanoff-Baym formalism for Bose superfluids 108

6.2 Hartree-Fock-Bogoliubov equations 111

6.3 Derivation of a kinetic equation with collisions 115

6.4 Collision integrals in the Hartree-Fock approximation 119

6.5 Generalized GP equation 122

6.6 Linearized collision integrals in collisionless theories 124

7 Kinetic equation for Bogoliubov thermal

excitations 129

7.1 Generalized kinetic equation 130

7.2 Kinetic equation in the Bogoliubov-Popov approximation 135

7.3 Comments on improved theory 143

8 Static thermal cloud approximation 146

8.1 Condensate collective modes at finite temperatures 147

8.2 Phenomenological GP equations with dissipation 157

8.3 Relation to Pitaevskii's theory of superfluid relaxation 160

9 Vortices and vortex lattices at finite temperatures 164

9.1 Rotating frames of reference: classical treatment 165

9.2 Rotating frames of reference: quantum treatment 170

9.3 Transformation of the kinetic equation 174

9.4 Zaremba-Nikuni-Griffin equations in a rotating frame 176

9.5 Stationary states 179

9.6 Stationary vortex states at zero temperature 181

9.7 Equilibrium vortex state at finite temperatures 184

9.8 Nonequilibrium vortex states 187

10 Dynamics at finite temperatures using the

moment method 198

10.1 Bose gas above TBEC 199

10.2 Scissors oscillations in a two-component superfluid 204

10.3 The moment of inertia and superfluid response 220

11 Numerical simulation of the ZNG equations 227

11.1 The generalized Gross-Pitaevskii equation 228

11.2 Collisionless particle evolution 231

11.3 Collisions 237

11.4 Self-consistent equilibrium properties 248

11.5 Equilibrium collision rates 252

12 Simulation of collective modes at finite temperature 256

12.1 Equilibration 257

12.2 Dipole oscillations 260

12.3 Radial breathing mode 263

12.4 Scissors mode oscillations 270

12.5 Quadrupole collective modes 279

12.6 Transverse breathing mode 286

13 Landau damping in trapped Bose-condensed gases 292

13.1 Landau damping in a uniform Bose gas 293

13.2 Landau damping in a trapped Bose gas 298

13.3 Numerical results for Landau damping 303

14 Landau's theory of superfluidity 309

14.1 History of two-fluid equations 309

14.2 First and second sound 312

14.3 Dynamic structure factor in the two-fluid region 317

15 Two-fluid hydrodynamics in a dilute Bose gas 322

15.1 Equations of motion for local equilibrium 324

15.2 Equivalence to the Landau two-fluid equations 331

15.3 First and second sound in a Bose-condensed gas 339

15.4 Hydrodynamic modes in a trapped normal Bose gas 345

16 Variational formulation of the Landau

two-fluid equations 349

16.1 Zilsel's variational formulation 350

16.2 The action integral for two-fluid hydrodynamics 356

16.3 Hydrodynamic modes in a trapped gas 359

16.4 Two-fluid modes in the BCS-BEC crossover at unitarity 370

17 The Landau-Khalatnikov two-fluid equations 371

17.1 The Chapman-Enskog solution of the kinetic equation 372

17.2 Deviation from local equilibrium 377

17.3 Equivalence to Landau-Khalatnikov two-fluid equations 387

17.4 The C12 collisions and the second viscosity coefficients 392

18 Transport coefficients and relaxation times 395

18.1 Transport coefficients in trapped Bose gases 396

18.2 Relaxation times for the approach to local equilibrium 405

18.3 Kinetic equations versus Kubo formulas 412

19 General theory of damping of hydrodynamic modes 414

19.1 Review of coupled equations for hydrodynamic modes 415

19.2 Normal mode frequencies 418

19.3 General expression for damping of hydrodynamic modes 420

19.4 Hydrodynamic damping in a normal Bose gas 424

19.5 Hydrodynamic damping in a superfluid Bose gas 428

Appendix A Monte Carlo calculation of collision rates 431

Appendix B Evaluation of transport coefficients:

technical details 436

Appendix C Frequency-dependent transport coefficients 444

Appendix D Derivation of hydrodynamic damping formula 448

References 451

Index 459

1995年，陷俘超冷原子气体玻色爱因斯坦凝聚的发现给玻色凝聚稀薄气体的理论和实验研究都带来了爆炸性的发展。本书提供了详细的超流玻色气体的非平衡态行为和双组分动力学理论。本书利用简单的微观模型，在无碰撞和碰撞为主的区域都给出了清晰明了的集体模式。
　　《有限温度玻色凝聚气体（英文影印版）》适合超冷原子物理，原子、分子和光物理，以及凝聚态物理领域的研究者和研究生阅读。

《有限温度玻色凝聚气体》是影印版英文专著，原书由剑桥大学出版社于2009年出版。玻色爱因斯坦凝聚在近代物理学中影响很远，而超冷原子等的研究也是近来非常受关注的方向，并已经催生了应用研究。本书对于意欲了解这一领域的读者非常有帮助，对于专业的研究者和研究生也是难得的参考书。