Many-body physics in condensed matter systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bologna
Ed. della Normale
2006
|
| Series: | Appunti
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 320 S. graph. Darst. |
| ISBN: | 9788876421921 8876421920 |
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MARC
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| 100 | 1 | |a Polini, Marco |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Many-body physics in condensed matter systems |c Marco Polini and Mario Tosi |
| 264 | 1 | |a Bologna |b Ed. della Normale |c 2006 | |
| 300 | |a XII, 320 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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|---|---|
| adam_text | Contents
Preface
XI
1
Introduction to many-body systems
1
1.1
Ideal Fermi gas and normal Fermi liquid
......... 1
1.2
Ideal
Bose gas, Bose
fluids and
superfluide
........ 2
1.3
Second quantization for
fermions
and bosons
...... 6
1.4
Hartree-Fock theory of the degenerate electron gas
... 9
1.4.1
Spin-polarized states of the electron gas
..... 10
1.5
Static screening and plasma oscillations
in the electron liquid
................... 11
1.6
Correlation energy and phase diagrams
of the electron liquids
................... 13
1.7
Bogoliubov theory for weakly coupled
Bose
gas
..... 16
1.8
Bose-Einstein condensation and superfluidity
...... 18
1.9
The Tonks-Girardeau gas and boson-fermion mapping
in dimensionality
D
= 1................. 20
2
Green s functions and linear response theory for
fermions
23
2.1
The single-particle Green s function and the self-energy
. 23
2.1.1
Ground-state energy related to self-energy
. ... 27
2.2
Quasiparticles and Landau s theory
of normal Fermi liquids
.................. 28
2.2.1
Landau free energy and effective mass
...... 29
2.3
Sound waves in liquid 3He
................ 32
2.4
Two-particle Green s functions and correlation functions
34
2.5
Linear density response and inelastic scattering spectra
. 36
2.5.1
Spectral representation and Kramers-Kronig re¬
lation
....................... 38
2.5.2
Power dissipation and fluctuation-dissipation the¬
orem
....................... 39
VI
2.5.3
Van Hove dynamic structure factor and inelastic
neutron scattering
................. 41
2.6
Transport phenomena and
Kubo
relations
........ 42
2.7
Generalized linear response
................ 44
Electron liquids in the normal state
45
3.1
Macroscopic properties and Landau Fermi-liquid
parameters
......................... 45
3.1.1
An effective Hamiltonian for quasiparticles
... 47
3.1.2
Quasiparticle self-energy and effective mass
. . . 50
3.2
Dielectric response and spin response of electron plasmas
52
3.2.1
Spin-resolved response
.............. 56
3.3
Lindhard susceptibility and
RPA
screening
........ 57
3.3.1
Diagrammatic routes to improvement on the
RPA
62
3.4
Local field factors for exchange and correlation
..... 63
3.4.1
Spin-resolved local field factors
......... 68
3.4.2
Effective electron-electron interactions
..... 70
3.5
Density functional theory at zero temperature
...... 72
3.6
Spin-density functional theory
.............. 75
3.7
Dynamic correlations and current-density
functional theory
..................... 76
3.7.1
Current response functions
............ 78
3.7.2
Approximate calculation of two-pair excitation
spectra
...................... 80
3.7.3
Time-dependent density functional theory
.... 81
3.7.4
Current-density functional theory
........ 83
Magnetism of conduction electrons and strongly correlated
electron fluids
87
4.1
Hubbard model and magnetic instability for itinerant
electrons
.......................... 87
4.2
Hubbard model in the atomic limit and the Kondo effect
91
4.2.1
Magnetic impurities in non-magnetic metals
... 92
4.3
Diamagnetism of conduction electrons
.......... 94
4.4
The two-dimensional electron liquid in high magnetic
fields
............................ 97
4.4.1
Composite
fermions
............... 102
4.5
Electrons in one dimension: the Luttinger liquid
..... 105
4.5.1
Adding the spin-
1/2
degree of freedom:
spin-charge separation
.............. 110
4.6
Electrons in one dimension:
spin pairing in the Luther-Emery liquid
.........
Ill
VII
4.7
Electrons
in
quantum
dots
................ 114
4.7.1
One-body densities
................ 118
4.7.2
Pair correlations
................. 119
Green s functions and linear response theory for bosons
123
5.1
Scattering length and the Lee-Huang-Yang expansion
. . 123
5.2
Single-particle Green s functions
and the Hugenholtz-Pines relation
............ 125
5.3
Linear response functions for
Bose
fluids
........ 128
5.4
Dynamical properties of
Bose
fluids
and the
Gavoret-Nozières
theorem
............ 130
5.4.1
Some simple approximations
........... 132
5.4.2
Damping processes
................ 133
5.5
Transverse response and superfluid density
........ 134
5.6
Vortices in quantum fluids
................ 135
5.7
Low-dimensional
Bose
fluids
............... 137
Gases of bosonic atoms in traps and optical lattices
141
6.1
The Gross-Pitaevskii equation for a confined
Bose gas
at
Τ
= 0.......................... 141
6.1.1
Ground state calculations
............. 143
6.1.2
Collective dynamics of a confined condensate
. . 145
6.2
Condensates in harmonic traps:
coherence and superfluidity
................ 147
6.2.1
Quantized vortices
................ 151
6.3
Condensates in optical lattices
.............. 154
6.4
Quantum dissipation in the Leggett-Caldeira model
... 161
6.5
Superfluid to Mott-insulator transition in atomic gases
.. 162
6.6
Bose-Einstein condensation with attractive interactions
. 166
6.7
Confined
Bose gas
at finite temperature:
the two-fluid semiclassical model
............. 168
6.8
Dynamical properties of condensates at finite temperature
170
6.9
Quantum kinetic theory for
Bose
gases
. . :....... 172
Confined Fermi gases and boson-fermion mixtures
177
7.1
Ideal Fermi gas under confinement
............ 177
7.1.1 Pauli
blocking
.................. 179
7.2
Dynamics of two-component Fermi gases:
the Vlasov-Landau equation
............... 180
7.2.1
Dynamical transition in colliding fermion clouds
182
7.3
Fermion superfluidity and the BCS-BEC crossover
... 183
7.3.1
The critical temperature
............. 185
VIII
7.3.2
Equilibrium properties
.............. 188
7.3.3
Dynamical properties
............... 189
7.4
High-Tc
superfluide:
the pseudogap phase
........ 193
7.5
Non-conventional superfluidity
in two-component Fermi gases
.............. 195
7.5.1
Inhomogeneous superfluidity
........... 198
7.6
A quantum phase transition in a trap:
demixing in boson-fermion mixtures
........... 201
7.6.1
Essential theory of a trapped mixture
...... 204
7.6.2
Demixing in a trapped mixture
.......... 206
7.6.3
The role of dimensionality
............ 209
7.7
Collapse in boson-fermion mixtures
with attractive interactions
................ 210
7.8
Collisionless dynamics of boson-fermion mixtures
... 211
Appendices
215
A Thomas-Fermi theory
217
В
Dependence of the plasma frequency
on dimensionality
219
С
The
Lehmann
spectral representation
223
D
Temperature Green s functions
225
E Perturbative
expansion for
fermions
and Feynman diagrams
229
E.
1
Interaction representation and perturbative expansion
. . 229
E.2 Wick theorem
....................... 231
E.3 Feynman diagrams
.................... 232
E.4 Dyson equation
...................... 235
E.5 Bethe-Salpeter equation and effective interactions
.... 236
E.6 Diagrammatic treatment of
RPA
density response
.... 238
E.7 Proper polarizability
................... 239
F
Linear response for free electrons in dimensionality
D
243
G
Strong scattering by impurities and the Friedel sum rule
247
H
Density functional theory at finite temperature
251
I Fractional statistics
255
IX
J
Edge states and dynamics
in quantum Hall systems
257
К
Diagrammatic expansion for bosons
and reduction to the Bogoliubov theory
261
L
Hydrodynamics of a superfluid
in the two-fluid model
265
M
Inelastic neutron scattering
from superfluid 4He
269
N
Charged boson fluids
275
О
Condensate formation and growth
281
P
From
3D
to ID for bosons in harmonic traps
283
Q
А ВЕС
acoustic analog of gravitational black holes
285
R Luttinger
and Luther-Emery phases
in confined one-dimensional Fermi gases
289
References
293
|
| adam_txt |
Contents
Preface
XI
1
Introduction to many-body systems
1
1.1
Ideal Fermi gas and normal Fermi liquid
. 1
1.2
Ideal
Bose gas, Bose
fluids and
superfluide
. 2
1.3
Second quantization for
fermions
and bosons
. 6
1.4
Hartree-Fock theory of the degenerate electron gas
. 9
1.4.1
Spin-polarized states of the electron gas
. 10
1.5
Static screening and plasma oscillations
in the electron liquid
. 11
1.6
Correlation energy and phase diagrams
of the electron liquids
. 13
1.7
Bogoliubov theory for weakly coupled
Bose
gas
. 16
1.8
Bose-Einstein condensation and superfluidity
. 18
1.9
The Tonks-Girardeau gas and boson-fermion mapping
in dimensionality
D
= 1. 20
2
Green's functions and linear response theory for
fermions
23
2.1
The single-particle Green's function and the self-energy
. 23
2.1.1
Ground-state energy related to self-energy
. . 27
2.2
Quasiparticles and Landau's theory
of normal Fermi liquids
. 28
2.2.1
Landau free energy and effective mass
. 29
2.3
Sound waves in liquid 3He
. 32
2.4
Two-particle Green's functions and correlation functions
34
2.5
Linear density response and inelastic scattering spectra
. 36
2.5.1
Spectral representation and Kramers-Kronig re¬
lation
. 38
2.5.2
Power dissipation and fluctuation-dissipation the¬
orem
. 39
VI
2.5.3
Van Hove dynamic structure factor and inelastic
neutron scattering
. 41
2.6
Transport phenomena and
Kubo
relations
. 42
2.7
Generalized linear response
. 44
Electron liquids in the normal state
45
3.1
Macroscopic properties and Landau Fermi-liquid
parameters
. 45
3.1.1
An effective Hamiltonian for quasiparticles
. 47
3.1.2
Quasiparticle self-energy and effective mass
. . . 50
3.2
Dielectric response and spin response of electron plasmas
52
3.2.1
Spin-resolved response
. 56
3.3
Lindhard susceptibility and
RPA
screening
. 57
3.3.1
Diagrammatic routes to improvement on the
RPA
62
3.4
Local field factors for exchange and correlation
. 63
3.4.1
Spin-resolved local field factors
. 68
3.4.2
Effective electron-electron interactions
. 70
3.5
Density functional theory at zero temperature
. 72
3.6
Spin-density functional theory
. 75
3.7
Dynamic correlations and current-density
functional theory
. 76
3.7.1
Current response functions
. 78
3.7.2
Approximate calculation of two-pair excitation
spectra
. 80
3.7.3
Time-dependent density functional theory
. 81
3.7.4
Current-density functional theory
. 83
Magnetism of conduction electrons and strongly correlated
electron fluids
87
4.1
Hubbard model and magnetic instability for itinerant
electrons
. 87
4.2
Hubbard model in the atomic limit and the Kondo effect
91
4.2.1
Magnetic impurities in non-magnetic metals
. 92
4.3
Diamagnetism of conduction electrons
. 94
4.4
The two-dimensional electron liquid in high magnetic
fields
. 97
4.4.1
Composite
fermions
. 102
4.5
Electrons in one dimension: the Luttinger liquid
. 105
4.5.1
Adding the spin-
1/2
degree of freedom:
spin-charge separation
. 110
4.6
Electrons in one dimension:
spin pairing in the Luther-Emery liquid
.
Ill
VII
4.7
Electrons
in
quantum
dots
. 114
4.7.1
One-body densities
. 118
4.7.2
Pair correlations
. 119
Green's functions and linear response theory for bosons
123
5.1
Scattering length and the Lee-Huang-Yang expansion
. . 123
5.2
Single-particle Green's functions
and the Hugenholtz-Pines relation
. 125
5.3
Linear response functions for
Bose
fluids
. 128
5.4
Dynamical properties of
Bose
fluids
and the
Gavoret-Nozières
theorem
. 130
5.4.1
Some simple approximations
. 132
5.4.2
Damping processes
. 133
5.5
Transverse response and superfluid density
. 134
5.6
Vortices in quantum fluids
. 135
5.7
Low-dimensional
Bose
fluids
. 137
Gases of bosonic atoms in traps and optical lattices
141
6.1
The Gross-Pitaevskii equation for a confined
Bose gas
at
Τ
= 0. 141
6.1.1
Ground state calculations
. 143
6.1.2
Collective dynamics of a confined condensate
. . 145
6.2
Condensates in harmonic traps:
coherence and superfluidity
. 147
6.2.1
Quantized vortices
. 151
6.3
Condensates in optical lattices
. 154
6.4
Quantum dissipation in the Leggett-Caldeira model
. 161
6.5
Superfluid to Mott-insulator transition in atomic gases
. 162
6.6
Bose-Einstein condensation with attractive interactions
. 166
6.7
Confined
Bose gas
at finite temperature:
the two-fluid semiclassical model
. 168
6.8
Dynamical properties of condensates at finite temperature
170
6.9
Quantum kinetic theory for
Bose
gases
. . :. 172
Confined Fermi gases and boson-fermion mixtures
177
7.1
Ideal Fermi gas under confinement
. 177
7.1.1 Pauli
blocking
. 179
7.2
Dynamics of two-component Fermi gases:
the Vlasov-Landau equation
. 180
7.2.1
Dynamical transition in colliding fermion clouds
182
7.3
Fermion superfluidity and the BCS-BEC crossover
. 183
7.3.1
The critical temperature
. 185
VIII
7.3.2
Equilibrium properties
. 188
7.3.3
Dynamical properties
. 189
7.4
High-Tc
superfluide:
the pseudogap phase
. 193
7.5
Non-conventional superfluidity
in two-component Fermi gases
. 195
7.5.1
Inhomogeneous superfluidity
. 198
7.6
A quantum phase transition in a trap:
demixing in boson-fermion mixtures
. 201
7.6.1
Essential theory of a trapped mixture
. 204
7.6.2
Demixing in a trapped mixture
. 206
7.6.3
The role of dimensionality
. 209
7.7
Collapse in boson-fermion mixtures
with attractive interactions
. 210
7.8
Collisionless dynamics of boson-fermion mixtures
. 211
Appendices
215
A Thomas-Fermi theory
217
В
Dependence of the plasma frequency
on dimensionality
219
С
The
Lehmann
spectral representation
223
D
Temperature Green's functions
225
E Perturbative
expansion for
fermions
and Feynman diagrams
229
E.
1
Interaction representation and perturbative expansion
. . 229
E.2 Wick theorem
. 231
E.3 Feynman diagrams
. 232
E.4 Dyson equation
. 235
E.5 Bethe-Salpeter equation and effective interactions
. 236
E.6 Diagrammatic treatment of
RPA
density response
. 238
E.7 Proper polarizability
. 239
F
Linear response for free electrons in dimensionality
D
243
G
Strong scattering by impurities and the Friedel sum rule
247
H
Density functional theory at finite temperature
251
I Fractional statistics
255
IX
J
Edge states and dynamics
in quantum Hall systems
257
К
Diagrammatic expansion for bosons
and reduction to the Bogoliubov theory
261
L
Hydrodynamics of a superfluid
in the two-fluid model
265
M
Inelastic neutron scattering
from superfluid 4He
269
N
Charged boson fluids
275
О
Condensate formation and growth
281
P
From
3D
to ID for bosons in harmonic traps
283
Q
А ВЕС
acoustic analog of gravitational black holes
285
R Luttinger
and Luther-Emery phases
in confined one-dimensional Fermi gases
289
References
293 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Polini, Marco Tosi, Mario P. |
| author_facet | Polini, Marco Tosi, Mario P. |
| author_role | aut aut |
| author_sort | Polini, Marco |
| author_variant | m p mp m p t mp mpt |
| building | Verbundindex |
| bvnumber | BV022532821 |
| classification_rvk | UP 1300 |
| ctrlnum | (OCoLC)493456173 (DE-599)BVBBV022532821 |
| dewey-full | 532 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532 |
| dewey-search | 532 |
| dewey-sort | 3532 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV022532821 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:07:15Z |
| indexdate | 2024-07-09T20:59:39Z |
| institution | BVB |
| isbn | 9788876421921 8876421920 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015739384 |
| oclc_num | 493456173 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-703 |
| physical | XII, 320 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Ed. della Normale |
| record_format | marc |
| series | Appunti |
| series2 | Appunti |
| spelling | Polini, Marco Verfasser aut Many-body physics in condensed matter systems Marco Polini and Mario Tosi Bologna Ed. della Normale 2006 XII, 320 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Appunti 4 Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Vielteilchentheorie (DE-588)4331960-9 s Festkörperphysik (DE-588)4016921-2 s DE-604 Tosi, Mario P. Verfasser aut Appunti 4 (DE-604)BV025597622 4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015739384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Polini, Marco Tosi, Mario P. Many-body physics in condensed matter systems Appunti Vielteilchentheorie (DE-588)4331960-9 gnd Festkörperphysik (DE-588)4016921-2 gnd |
| subject_GND | (DE-588)4331960-9 (DE-588)4016921-2 |
| title | Many-body physics in condensed matter systems |
| title_auth | Many-body physics in condensed matter systems |
| title_exact_search | Many-body physics in condensed matter systems |
| title_exact_search_txtP | Many-body physics in condensed matter systems |
| title_full | Many-body physics in condensed matter systems Marco Polini and Mario Tosi |
| title_fullStr | Many-body physics in condensed matter systems Marco Polini and Mario Tosi |
| title_full_unstemmed | Many-body physics in condensed matter systems Marco Polini and Mario Tosi |
| title_short | Many-body physics in condensed matter systems |
| title_sort | many body physics in condensed matter systems |
| topic | Vielteilchentheorie (DE-588)4331960-9 gnd Festkörperphysik (DE-588)4016921-2 gnd |
| topic_facet | Vielteilchentheorie Festkörperphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015739384&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV025597622 |
| work_keys_str_mv | AT polinimarco manybodyphysicsincondensedmattersystems AT tosimariop manybodyphysicsincondensedmattersystems |