Bose-Einstein condensation:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
2007
|
| Edition: | 1. publ., reprint. |
| Series: | The international series of monographs on physics
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 382 S. Ill., graph. Darst. |
| ISBN: | 0198507194 9780198507192 |
Staff View
MARC
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| 245 | 1 | 0 | |a Bose-Einstein condensation |c Lev Pitaevskii ; Sandro Stringari |
| 250 | |a 1. publ., reprint. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 2007 | |
| 300 | |a X, 382 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1
Introduction
ι
PART I
2
Long-range order, symmetry breaking and order
parameter
7
2.1
One-body density matrix and long-range order
7
2.2
Order parameter
ц
3
The ideal
Bose gas
13
3.1
The ideal
Bose
gas in the grand canonical ensemble
13
3.2
The ideal
Bose gas
in the box
17
3.3
Fluctuations of the single-particle occupation numbers
24
4
The weakly-interacting
Bose gas
26
4.1
Lowest-order approximation: ground state energy and
equation of state
26
4.2
Higher-order approximation: excitation spectrum and
quantum fluctuations
30
4.3
Particles and elementary excitations
33
5
Nonuniform
Bose
gases at zero temperature
38
5.1
The Gross-Pitaevskii equation
38
5.2
Thomas-Fermi limit
43
5.3
Vortex iine in the weakly-interacting
Bose gas
44
5.4
Vortex rings
47
5.5 Solitons 52
5.6
Small-amplitude oscillations
55
5.7
Quantization and elementary excitations
60
>
Superfluidity
63
6.1
Landau s criterion of superfluidity
63
6.2
Bose-Einstein condensation and superfluidity
67
6.3
Hydrodynamic theory of
superfluide: zero
temperature
68
6.4
Quantum hydrodynamics
69
6.5
Beliaev decay of phonons
72
6.6
Two-fluid hydrodynamics: first and second sound
74
6.7
Fluctuations of the phase
78
6.8
Rotation of superfluids
82
viii CONTENTS
7
Linear
response
function
87
7.1
Dynamic structure factor and sum rules
87
7.2
Density response function
92
7.3
Current response function
96
7.4
General inequalities
98
7.5
Response function of the ideal
Bose gas
102
7.6
Response function of the weakly-interacting
Bose gas
104
7.7
Response function of
a
nonuniform
Bose
gas 107
8
Superfluid
4Не
108
8.1
Introduction
108
8.2
Elementary excitations and dynamic structure factor
109
8.3
Thermodynamic properties
116
8.4
Quantized vortices
118
8.5
Momentum distribution and Bose-Einstein condensation
122
PART II
9
Atomic gases: collisions and trapping
129
9.1
Metastability and the role of collisions
129
9.2
Low-energy collisions and scattering length
131
9.3
Zeeman
effect and magnetic trapping
138
9.4
Interaction with the radiation field and optical traps
144
10
The ideal
Bose
gas in the harmonic trap
147
10.1
Condensate fraction and critical temperature
147
10.2
Density of single-particle states and thermodynamics
150
10.3
Density and momentum distribution
152
10.4
Thermodynamic limit
155
10.5
Release of the trap and expansion of the gas
155
10.6
Bose-Einstein condensation in deformed traps
157
10.7
Adiabatic formation of
ВЕС
with nonharmonic traps
158
11
Ground state of a trapped condensate
161
11.1
Introduction
161
11.2
An instructive example: the box potential
161
11.3
Interacting condensates in harmonic traps: density and
momentum distribution
163
11.4
Energy, chemical potential and virial theorem
167
11.5
Finite-size corrections to the Thomas-Fermi limit
169
11.6
Attractive forces
174
CONTENTS ix
12 Dynamics
of a trapped condensate
177
12.1
Introduction
177
12.2
Collective oscillations
177
12.3
Repulsive forces and the Thomas-Fermi limit
180
12.4
Sum rule approach: from repulsive to attractive forces
186
12.5
Finite-size corrections to the Thomas-Fermi limit
189
12.6
Beyond mean field corrections
190
12.7
Large-amplitude oscillations
192
12.8
Expansion of the condensate
194
12.9
Dynamic structure factor
197
12.10
Collective versus single-particle excitations
210
12.11
Mixtures of Bose-Einstein condensates
214
13
Thermodynamics of a trapped
Bose gas
222
13.1
Role of interactions, scaling and the thermodynamic limit
222
13.2
The Hartree-Fock approximation
225
13.3
Shift of the critical temperature
229
13.4
Critical region near Tc
230
13.5
Below Tc
232
13.6
Collective oscillations at a finite temperature
239
14
Rotation of a trapped
Bose gas
244
14.1
Introduction: superfluidity of a trapped gas
244
14.2
Moment of inertia
245
14.3
Scissors mode
249
14.4
Expanding a rotating condensate
251
14.5
Rotation at high angular velocities
252
14.6
Quantized vortices
256
14.7
Vortices, angular momentum and collective oscillations
263
14.8
Stability and precession of the vortex line
269
15
Coherence, interference and the
Josephson
effect
274
15.1
Introduction
274
15.2
Coherence and one-body density matrix
275
15.3
Interference between two condensates
278
15.4
Josephson
effect
287
15.5
Quantization of the
Josephson
equations
291
15.6
Decoherence and phase spreading
296
15.7
Boson Hubbard Hamiltonian
298
16
Bose—
Einstein condensation in optical lattices
303
16.1
Equilibrium properties
303
16.2
Energy bands and Bloch oscillations
309
16.3
Elementary excitations
314
16.4
Quantum fluctuations in optical traps
320
χ
CONTENTS
17
Bose-Eînstein condensation
in low dimensions
323
17.1
Introduction
323
17.2
One-dimensional
Bose gas:
mean field theory
323
17.3
One-dimensional interacting
Bose gas:
beyond mean field
331
17.4
Two-dimensional
Bose gas
at zero temperature
339
17.5
Two-dimensional
Bose gas
at finite temperatures
341
18
Atomic Fermi gases in traps
346
18.1
Introduction
346
18.2
Ideal Fermi gas in the harmonic potential
348
18.3
Role of interactions, collective frequencies and collisional
effects
352
18.4
The BCS transition
358
18.5
Effects of superfluidity on a trapped Fermi gas
364
References
367
Index
381
|
| adam_txt |
CONTENTS
1
Introduction
ι
PART I
2
Long-range order, symmetry breaking and order
parameter
7
2.1
One-body density matrix and long-range order
7
2.2
Order parameter
ц
3
The ideal
Bose gas
13
3.1
The ideal
Bose
gas in the grand canonical ensemble
13
3.2
The ideal
Bose gas
in the box
17
3.3
Fluctuations of the single-particle occupation numbers
24
4
The weakly-interacting
Bose gas
26
4.1
Lowest-order approximation: ground state energy and
equation of state
26
4.2
Higher-order approximation: excitation spectrum and
quantum fluctuations
30
4.3
Particles and elementary excitations
33
5
Nonuniform
Bose
gases at zero temperature
38
5.1
The Gross-Pitaevskii equation
38
5.2
Thomas-Fermi limit
43
5.3
Vortex iine in the weakly-interacting
Bose gas
44
5.4
Vortex rings
47
5.5 Solitons 52
5.6
Small-amplitude oscillations
55
5.7
Quantization and elementary excitations
60
>
Superfluidity
63
6.1
Landau's criterion of superfluidity
63
6.2
Bose-Einstein condensation and superfluidity
67
6.3
Hydrodynamic theory of
superfluide: zero
temperature
68
6.4
Quantum hydrodynamics
69
6.5
Beliaev decay of phonons
72
6.6
Two-fluid hydrodynamics: first and second sound
74
6.7
Fluctuations of the phase
78
6.8
Rotation of superfluids
82
viii CONTENTS
7
Linear
response
function
87
7.1
Dynamic structure factor and sum rules
87
7.2
Density response function
92
7.3
Current response function
96
7.4
General inequalities
98
7.5
Response function of the ideal
Bose gas
102
7.6
Response function of the weakly-interacting
Bose gas
104
7.7
Response function of
a
nonuniform
Bose
gas 107
8
Superfluid
4Не
108
8.1
Introduction
108
8.2
Elementary excitations and dynamic structure factor
109
8.3
Thermodynamic properties
116
8.4
Quantized vortices
118
8.5
Momentum distribution and Bose-Einstein condensation
122
PART II
9
Atomic gases: collisions and trapping
129
9.1
Metastability and the role of collisions
129
9.2
Low-energy collisions and scattering length
131
9.3
Zeeman
effect and magnetic trapping
138
9.4
Interaction with the radiation field and optical traps
144
10
The ideal
Bose
gas in the harmonic trap
147
10.1
Condensate fraction and critical temperature
147
10.2
Density of single-particle states and thermodynamics
150
10.3
Density and momentum distribution
152
10.4
Thermodynamic limit
155
10.5
Release of the trap and expansion of the gas
155
10.6
Bose-Einstein condensation in deformed traps
157
10.7
Adiabatic formation of
ВЕС
with nonharmonic traps
158
11
Ground state of a trapped condensate
161
11.1
Introduction
161
11.2
An instructive example: the box potential
161
11.3
Interacting condensates in harmonic traps: density and
momentum distribution
163
11.4
Energy, chemical potential and virial theorem
167
11.5
Finite-size corrections to the Thomas-Fermi limit
169
11.6
Attractive forces
174
CONTENTS ix
12 Dynamics
of a trapped condensate
177
12.1
Introduction
177
12.2
Collective oscillations
177
12.3
Repulsive forces and the Thomas-Fermi limit
180
12.4
Sum rule approach: from repulsive to attractive forces
186
12.5
Finite-size corrections to the Thomas-Fermi limit
189
12.6
Beyond mean field corrections
190
12.7
Large-amplitude oscillations
192
12.8
Expansion of the condensate
194
12.9
Dynamic structure factor
197
12.10
Collective versus single-particle excitations
210
12.11
Mixtures of Bose-Einstein condensates
214
13
Thermodynamics of a trapped
Bose gas
222
13.1
Role of interactions, scaling and the thermodynamic limit
222
13.2
The Hartree-Fock approximation
225
13.3
Shift of the critical temperature
229
13.4
Critical region near Tc
230
13.5
Below Tc
232
13.6
Collective oscillations at a finite temperature
239
14
Rotation of a trapped
Bose gas
244
14.1
Introduction: superfluidity of a trapped gas
244
14.2
Moment of inertia
245
14.3
Scissors mode
249
14.4
Expanding a rotating condensate
251
14.5
Rotation at high angular velocities
252
14.6
Quantized vortices
256
14.7
Vortices, angular momentum and collective oscillations
263
14.8
Stability and precession of the vortex line
269
15
Coherence, interference and the
Josephson
effect
274
15.1
Introduction
274
15.2
Coherence and one-body density matrix
275
15.3
Interference between two condensates
278
15.4
Josephson
effect
287
15.5
Quantization of the
Josephson
equations
291
15.6
Decoherence and phase spreading
296
15.7
Boson Hubbard Hamiltonian
298
16
Bose—
Einstein condensation in optical lattices
303
16.1
Equilibrium properties
303
16.2
Energy bands and Bloch oscillations
309
16.3
Elementary excitations
314
16.4
Quantum fluctuations in optical traps
320
χ
CONTENTS
17
Bose-Eînstein condensation
in low dimensions
323
17.1
Introduction
323
17.2
One-dimensional
Bose gas:
mean field theory
323
17.3
One-dimensional interacting
Bose gas:
beyond mean field
331
17.4
Two-dimensional
Bose gas
at zero temperature
339
17.5
Two-dimensional
Bose gas
at finite temperatures
341
18
Atomic Fermi gases in traps
346
18.1
Introduction
346
18.2
Ideal Fermi gas in the harmonic potential
348
18.3
Role of interactions, collective frequencies and collisional
effects
352
18.4
The BCS transition
358
18.5
Effects of superfluidity on a trapped Fermi gas
364
References
367
Index
381 |
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| id | DE-604.BV023056208 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:26:50Z |
| indexdate | 2024-07-09T21:09:57Z |
| institution | BVB |
| isbn | 0198507194 9780198507192 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016259498 |
| oclc_num | 254930386 |
| open_access_boolean | |
| owner | DE-384 |
| owner_facet | DE-384 |
| physical | X, 382 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Clarendon Press |
| record_format | marc |
| series | The international series of monographs on physics |
| series2 | The international series of monographs on physics Oxford science publications |
| spelling | Pitaevskij, Lev P. 1933-2022 Verfasser (DE-588)107927683 aut Bose-Einstein condensation Lev Pitaevskii ; Sandro Stringari 1. publ., reprint. Oxford Clarendon Press 2007 X, 382 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The international series of monographs on physics 116 Oxford science publications Bose-Einstein-Kondensation (DE-588)4402897-0 gnd rswk-swf Bose-Einstein-Kondensation (DE-588)4402897-0 s DE-604 Stringari, Sandro 1949- Verfasser (DE-588)151622094 aut The international series of monographs on physics 116 (DE-604)BV000106406 116 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016259498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pitaevskij, Lev P. 1933-2022 Stringari, Sandro 1949- Bose-Einstein condensation The international series of monographs on physics Bose-Einstein-Kondensation (DE-588)4402897-0 gnd |
| subject_GND | (DE-588)4402897-0 |
| title | Bose-Einstein condensation |
| title_auth | Bose-Einstein condensation |
| title_exact_search | Bose-Einstein condensation |
| title_exact_search_txtP | Bose-Einstein condensation |
| title_full | Bose-Einstein condensation Lev Pitaevskii ; Sandro Stringari |
| title_fullStr | Bose-Einstein condensation Lev Pitaevskii ; Sandro Stringari |
| title_full_unstemmed | Bose-Einstein condensation Lev Pitaevskii ; Sandro Stringari |
| title_short | Bose-Einstein condensation |
| title_sort | bose einstein condensation |
| topic | Bose-Einstein-Kondensation (DE-588)4402897-0 gnd |
| topic_facet | Bose-Einstein-Kondensation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016259498&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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