Preface
1 Overview and introduction
1.1 Historical overview of Bose superfluids
1.2 Summary of chapters
2 Condensate dynamics at
2.1 Gross Pita~vskii (GP) equation
2.2 Bogoliubov equations for condensate fluctuations
3 Coupled equations for the condensate and thermal cloud
3.1 Generalized GP equation for the condensate
3.2 Boltzmann equation for the noncondensate atoms
3.3 Solutions in thermal equilibrium
3.4 Region of validity of the ZNG equations
4 Green's functions and self-energy approximations
4.1 Overview of Green's function approach
4.2 Nonequilibrium Green's functions in normal systems
4.3 Green's functions in a Bose-condensed gas
4.4 Classification of self-energy approximations
4.5 Dielectric formalism
5 The Beliaev and the time-dependent HFB approximations
5.1 Hartree-Fock Bogoliubov self-energies
5.2 Beliaev self-energy approximation
5.3 Beliaev as time-dependent HFB
5.4 Density response in the Beliaev-Popov approximation
6 Kadanoff-Baym derivation of the ZNG equations
6.1 Kadanoff Baym formalism for Bose superfiuids
6.2 Hartree Fock Bogoliubov equations
6.3 Derivation of a kinetic equation with collisions
6.4 Collision integrals in the Hartree-Fock approximation
6.5 Generalized GP equation
6.6 Linearized collision integrals in collisionless theories
7 Kinetic equation for Bogoliubov thermal excitations
7.1 Generalized kinetic equation
7.2 Kinetic equation in the Bogoliubov Popov approximation
7.3 Comments on improved theory
8 Static thermal cloud approximation
8.1 Condensate collective modes at finite temperatures
8.2 Phenomenological GP equations with dissipation
8.3 Relation to Pitaevskii's theory of superfluid relaxation
9 Vortices and vortex lattices at finite temperatures
9.1 Rotating frames of reference: classical treatment
9.2 Rotating frames of reference: quantum treatment
9.3 Transformation of the kinetic equation
9.4 Zaremba-Nikuni Griffin equations in a rotating frame
9.5 Stationary states
9.6 Stationary vortex states at zero temperature
9.7 Equilibrium vortex state at finite temperatures
9.8 Nonequilibrium vortex states
l0 Dynamics at finite temperatures using the moment method
10.1 Bose gas above TBmC
10.2 Scissors oscillations in a two-component superfluid
10.3 The moment of inertia and superfluid response
11 Numerical simulation of the ZNG equations
11.1 The generalized Gross Pitaevskii equation
11.2 Collisionless particle evolution
11.3 Collisions
11.4 Self-consistent equilibrium properties
11.5 Equilibrium collision rates
12 Simulation of collective modes at finite temperature
12.1 Equilibration
12.2 Dipole oscillations
12.3 Radial breathing mode
12.4 Scissors mode oscillations
12.5 Quadrupole collective modes
12.6 Transverse breathing mode
13 Landau damping in trapped Base-condensed gases
13.1 Landau damping in a uniform Bose gas
13.2 Landau dmnping in a trapped Bose gas
13.3 Numerical results for Landau damping
14 Landau's theory of superfluidity
14.1 History of two-fluid equations
14.2 First and second sound
14.3 Dynamic structure factor in the two-fluid region
15 Two-fluid hydrodynamics in a dilute Bose gas
15.1 Equations of motion for local equilibrium
15.2 Equivalence to the Landau two-fluid equations
15.3 First and second sound in a Bose-condensed gas
15.4 Hydrodynamic modes in a trapped normal Bose gas
16 Variational formulation of the Landau two-fluld equations
16.1 Zilscl's variational formulation
16.2 The action integral for two-fluid hydrodynamics
16.3 Hydrodynamic modes in a trapped gas
16.4 Two-fluid modes in the BCS BEC crossover at uuitarity
17 The Landau Khalatnikov two-fluid equations
17.1 The Chapman-Enskog solution of the kinetic equation
17.2 Deviation from local equilibrium
17.3 Equivalence to Landau Khalatnikov two-fluid equations
17.4 The C12 collisions and the second viscosity coefficients
18 Transport coefficients and relaxation times
18.1 Transport coefficients in trapped Bose gases
18.2 Relaxation times for the approach to local equilibrium
18.3 Kinetic equations versus Kubo formulas
19 General theory of damping of hydrodynamic modes
19.1 Review of coupled equations for hydrodynamic modes
19.2 Normal mode frequencies
19.3 General expression for damping of hydrodynamic modes
19.4 Hydrodynamic damping in a normal Bose gas
19.5 Hydrodynamic damping in a superfluid Bose gas
Appendix A Monte Carlo calculation of collision rates
Appendix B Evaluation of transport coefficients: technical details
Appendix C Frequency-dependent transport coefficients
Appendix D Derivation of hydrodynamic damping formula
References
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