正版 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 Greens functions and self-energy approximations 54
4.1 Overview of Greens function approach 54
4.2 Nonequilibrium Greens functions in normal systems 58
4.3 Greens 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 Pitaevskiis 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 Landaus 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 Zilsels 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。 本书适合超冷原子物理，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。

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。格里芬、二国彻郎、扎伦巴编写的《有限温度玻色凝聚气体(影印版)》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。本书适合超冷原子物理，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。