Bose-condensed gases at finite temperatures:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 462 S. graph. Darst. |
| ISBN: | 9780521837026 0521837022 |
Staff View
MARC
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| 100 | 1 | |a Griffin, Allan |e Verfasser |0 (DE-588)137680767 |4 aut | |
| 245 | 1 | 0 | |a Bose-condensed gases at finite temperatures |c Allan Griffin ; Tetsuro Nikuni ; Eugene Zaremba |
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XI, 462 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Bose-Einstein condensation | |
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| 650 | 4 | |a Bose-Einstein condensation | |
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| 700 | 1 | |a Nikuni, Tetsuro |e Verfasser |4 aut | |
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Record in the Search Index
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| adam_text | Contents
Preface
раде їх
1
Overview and introduction
1
1.1
Historical overview of
Bose
superfluide
9
1.2
Summary of chapters
12
2
Condensate dynamics at
Τ
= 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
vi
Contents
6
Kadanoff-Baym
derivation of the ZNG equations
107
6.1
Kadanoff-Baym formalism for
Bose
superfluide
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
Contents
vii
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
С и
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
viii Contents
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
В
Evaluation of transport coefficients:
technical details
436
Appendix
С
Frequency-dependent transport coefficients
444
Appendix
D
Derivation of hydrodynamic damping formula
448
References
451
Index
459
|
| adam_txt |
Contents
Preface
раде їх
1
Overview and introduction
1
1.1
Historical overview of
Bose
superfluide
9
1.2
Summary of chapters
12
2
Condensate dynamics at
Τ
= 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
vi
Contents
6
Kadanoff-Baym
derivation of the ZNG equations
107
6.1
Kadanoff-Baym formalism for
Bose
superfluide
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
Contents
vii
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
С и
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
viii Contents
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
В
Evaluation of transport coefficients:
technical details
436
Appendix
С
Frequency-dependent transport coefficients
444
Appendix
D
Derivation of hydrodynamic damping formula
448
References
451
Index
459 |
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| author | Griffin, Allan Nikuni, Tetsuro Zaremba, Eugene 1946- |
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| id | DE-604.BV035093373 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:11:24Z |
| indexdate | 2024-07-09T21:22:02Z |
| institution | BVB |
| isbn | 9780521837026 0521837022 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016761455 |
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| physical | XI, 462 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Griffin, Allan Verfasser (DE-588)137680767 aut Bose-condensed gases at finite temperatures Allan Griffin ; Tetsuro Nikuni ; Eugene Zaremba Cambridge Cambridge Univ. Press 2009 XI, 462 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bose-Einstein condensation Bose-Einstein gas Bose-Gas (DE-588)4146392-4 gnd rswk-swf Bose-Einstein-Kondensation (DE-588)4402897-0 gnd rswk-swf Bose-Einstein-Kondensation (DE-588)4402897-0 s DE-604 Bose-Gas (DE-588)4146392-4 s Nikuni, Tetsuro Verfasser aut Zaremba, Eugene 1946- Verfasser (DE-588)137681062 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016761455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griffin, Allan Nikuni, Tetsuro Zaremba, Eugene 1946- Bose-condensed gases at finite temperatures Bose-Einstein condensation Bose-Einstein gas Bose-Gas (DE-588)4146392-4 gnd Bose-Einstein-Kondensation (DE-588)4402897-0 gnd |
| subject_GND | (DE-588)4146392-4 (DE-588)4402897-0 |
| title | Bose-condensed gases at finite temperatures |
| title_auth | Bose-condensed gases at finite temperatures |
| title_exact_search | Bose-condensed gases at finite temperatures |
| title_exact_search_txtP | Bose-condensed gases at finite temperatures |
| title_full | Bose-condensed gases at finite temperatures Allan Griffin ; Tetsuro Nikuni ; Eugene Zaremba |
| title_fullStr | Bose-condensed gases at finite temperatures Allan Griffin ; Tetsuro Nikuni ; Eugene Zaremba |
| title_full_unstemmed | Bose-condensed gases at finite temperatures Allan Griffin ; Tetsuro Nikuni ; Eugene Zaremba |
| title_short | Bose-condensed gases at finite temperatures |
| title_sort | bose condensed gases at finite temperatures |
| topic | Bose-Einstein condensation Bose-Einstein gas Bose-Gas (DE-588)4146392-4 gnd Bose-Einstein-Kondensation (DE-588)4402897-0 gnd |
| topic_facet | Bose-Einstein condensation Bose-Einstein gas Bose-Gas Bose-Einstein-Kondensation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016761455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT griffinallan bosecondensedgasesatfinitetemperatures AT nikunitetsuro bosecondensedgasesatfinitetemperatures AT zarembaeugene bosecondensedgasesatfinitetemperatures |