Modern many-particle physics: atomic gases, nanostructures and quantum liquids
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 582 S. graph. Darst. |
| ISBN: | 9812709312 9789812709318 9789812709325 9812709320 |
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| 100 | 1 | |a Lipparini, Enrico |e Verfasser |0 (DE-588)138257043 |4 aut | |
| 245 | 1 | 0 | |a Modern many-particle physics |b atomic gases, nanostructures and quantum liquids |c Enrico Lipparini |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XIV, 582 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Many-body problem | |
| 650 | 4 | |a Particles (Nuclear physics) | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Quantentheorie | |
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| 689 | 0 | |5 DE-604 | |
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| adam_text | Contents
Preface
v
Preface
to the Second Edition
vii
Chapter
1
The Independent-Particle Model
1
1.1
Introduction
.................................. 1
1.2
Bosons
..................................... 2
1.3
Fermions
................................... 3
1.4
Matrix Elements of One-Body Operators
................. 6
1.5
Matrix Elements of Two-Body Operators
................. 8
1.6
Density Matrices
............................... 10
1.7
The Ideal
Bose
Gas Confined in a Harmonic Potential
.......... 12
1.8
The Fermi Gas
................................ 14
1.8.1
Excited States
............................ 19
1.8.2
Polarized Fermi Gas
......................... 23
1.8.3
The Fermi Gas in Two Dimensions with Rashba Interaction
... 24
1.9
Finite Temperature and Quasiparticles
................... 25
Chapter
2
The Hartree-Pock Theory
35
2.1
Introduction
.................................. 35
2.2
The Hartree-Fock Method for
Fermions
.................. 36
2.2.1
Examples of Physical Systems Treated by the Hartree-Fock
Method
................................ 40
2.2.2
Examples of Infinite Systems Treated by the Hartree-Fock
Method
................................ 51
2.3
The Hartree-Fock Method for Bosons
................... 55
2.4
The Gross-Pitaevskii Equations
....................... 56
2.5
Hartree-Fock in Second Quantization Language
.............. 58
2.6
Hartree-Fock at Finite Temperature
.................... 60
2.7
Hartree-Fock-Bogoliubov and BCS
..................... 65
2.8
Appendix: Second Quantization
....................... 69
x
Contents
Chapter
3
The Brueckner-Hartree-Fock Theory
76
3.1
Introduction
.................................. 76
3.2
The Lippman-Schwinger Equation
..................... 76
3.3
The Bethe-Goldstone Equation
....................... 78
3.4
Examples of Application of the BHF Theory
............... 80
3.4.1
The One-Dimensional Fermion System
............... 80
3.4.2
Ultracold Highly Polarized Fermi Gases
.............. 81
3.5
Numerical Results of BHF Calculation in Different Systems
....... 84
3.6
The
g
Matrix for the 2D Electron Gas
................... 86
3.6.1
Decomposition in Partial Waves
.................. 87
3.6.2
The Separable Approximation
................... 91
3.6.3
The
g
Matrix Expansion
....................... 95
3.6.4
Numerical Results and Discussion
................. 98
3.7
The
g
Matrix for Confined Electron Systems
............... 100
3.7.1
Effective Interaction in Confined Electron Systems
........ 108
3.8
The BBP Method
.............................. 110
3.8.1
Appendix
............................... 113
Chapter
4
The Density Functional Theory
116
4.1
Introduction
.................................. 116
4.2
The Density Functional Formalism
..................... 116
4.3
Examples of Application of the Density Functional Theory
....... 118
4.3.1
The Thomas-Fermi Theory for the Atom
............. 118
4.3.2
The Gross-Pitaevskii Theory for the Ground State of a Dilute
Gas of Bosons
............................ 120
4.3.3
The Thomas Fermi Approximation for the Fermi Gas Confined
in a Harmonic Potential
....................... 121
4.4
The Kohn-Sham Equations
......................... 125
4.5
The Local Density Approximation for the Exchange-Correlation Energy
127
4.6
The Local Spin Density Approximation (LSDA)
............. 128
4.7
Inclusion of Current Terms in the DFT (CDFT)
............. 131
4.8
The Ensemble Density Functional Theory (EDFT)
............ 134
4.9
The DFT for Strongly Correlated Systems: Nuclei and Helium
..... 135
4.10
The DFT for Mixed Systems
........................ 145
4.11
Symmetries and Mean Field Theories
................... 150
Chapter
5
The Confined 2D Electron Gas in a Magnetic Field
159
5.1
Introduction
.................................. 159
5.2
Quantum Dots in a Magnetic Field
..................... 159
5.2.1
The
ω0
»
шс
Case
.......................... 160
5.2.2
The
шс
>
ω0
Case
.......................... 161
5.2.3
The Maximum Density Droplet
(MDD)
State
........... 163
5.3
The Fractional Regime
............................ 165
Contents xi
5.4
The Hall Effect
................................ 167
5.5
Elliptical Quantum Dots
........................... 169
5.5.1
Analogies with the Bose-Einstein Condensate in a
Rotating Trap
............................ 173
5.6
The DFT for Quantum Dots in a Magnetic Field
............. 175
5.7
Quantum Wires
................................ 189
5.8
The Aharanov-Bohm Effect and Quantum Rings
............. 194
5.9
Quantum Molecules
............................. 200
5.9.1
The
В
= 0
Case
........................... 201
5.9.2
Β φ
0................................. 206
Chapter
6
Spin-Orbit Coupling in the Confined 2D Electron Gas
218
6.1
Spin-Orbit Coupling in Semiconductors
.................. 219
6.2
Spin-Orbit Effects on Single-Particle States in Quantum Wells
..... 220
6.2.1
The Case in Which Either
Ад
= 0
or D
= 0............ 221
6.2.2
The General Case Where XR
φ
0
and D
φ
0............ 223
6.3
Single-Particle Level Transitions in Quantum Wells
............ 227
6.4
The Magnetic Field in Plane
........................ 230
6.5
Spin-Orbit Effects on Single-Particle States in Quantum Dots
..... 231
6.5.1
Single-Particle Transitions in Dots
................. 237
6.6
Spin-Orbit Effects on Single-Particle States in Quantum Wires
..... 241
6.7
The LSDA with Spin-Orbit Coupling
................... 245
6.8
Comparison with Experiments in Quantum Wells
............. 252
6.9
LSDA Results and Comparison with Experiments for Quantum Dots
. . 256
6.10
LSDA Results for Quantum Wires
..................... 271
6.11
Appendix A
.................................. 280
6.12
Appendix
В
.................................. 281
Chapter
7
Monte Carlo Methods
285
7.1
Introduction
.................................. 285
7.2
Standard Quadrature Methods
....................... 285
7.3
Random Variable Distributions and the Central Limit Theorem
..... 287
7.4
Sampling Techniques
............................. 289
7.4.1
The Inversion Rule
.......................... 289
7.4.2
The Rejection Method
........................ 290
7.4.3
Markov Chains
............................ 290
7.5
The Metropolis Algorithm [M(RT)2}
.................... 294
7.6
Variational Monte Carlo for Liquid 4He
.................. 296
7.7
Variational Monte Carlo for
Fermions
................... 298
7.8
Optimization of Variational Wave Functions
................ 301
7.9
Monte Carlo Methods and Quantum Mechanics
.............. 304
7.10
Propagation of a State in Imaginary Time
................. 305
7.11
The
Schrödinger
Equation in Imaginary Time
............... 306
xii Contents
7.12
Importance
Sampling
........................... 308
7.13
Importance Sampling and Green Functions
............... 311
7.14
Fermion Systems and the Sign Problem
................. 313
7.15
Two Examples of DMC Calculations in Many-Body Systems
..... 316
7.15.1
The Equation of State of Diluted Ultracold Fermi Gases in
the BEC-BCS Crossover
....................316
7.15.2
Many-Nucleon Systems
.....................318
Chapter
8
The Linear Response Function Theory
325
8.1
Introduction
................................ 325
8.2
The General Formalism
.......................... 328
8.3
The Linear Response Function and Sum Rules
............. 332
8.4
Finite Temperature
............................. 336
8.5
The Density Response
........................... 338
8.6
The Density Response for Noninteracting Homogeneous Systems
. . . 342
8.7
The Current Response to an Electromagnetic Field
........... 347
8.8
The Conductivity of Quantum Wires
................... 352
8.9
Magnetoconductivity
........................... 360
8.9.1
The Kohn Theorem
....................... 360
8.9.2
Magnetoconductivity and the Quantum Hall Effect
...... 363
8.10
The Larmor Theorem
........................... 367
8.10.1
Electron Spin Precession with Rashba Spin-Orbit Coupling
. 367
8.11
Deviations from Kohn and Larmor Theorems Due to
Spin-Orbit Coupling
............................ 369
8.11.1
Spin-Orbit Splitting of Cyclotron Resonance
......... 369
8.11.2
Spin Splitting of Landau Levels
................. 374
8.12
Spin-Hall Conductivity
........................... 375
8.12.1
The Spin-Hall Effect at a Finite Magnetic Field
....... 377
8.12.2
Spin-Hall Conductivity Without SO Coupling
......... 378
8.12.3
Influence of the SO Coupling on the Spin-Hall Conductivity
. 379
8.13
Hall Conductivity in Graphene
...................... 382
Chapter
9
The Linear Response Function in Different Models
387
9.1
The Linear Response Function in Landau Theory
............387
9.2
Time Dependent
Hartree
(TDH) for Homogeneous Systems: The
RPA
401
9.3
TDH for the Density Matrix and the Landau Equations
........405
9.4
The
RPA
for the Electron Gas in Different Dimensions: The Plasmon
407
9.5
The
RPA
for Bosons
............................413
9.6
The Time-Dependent Gross-Pitaevskii Theory
.............417
9.7
Time-Dependent Hartree^Fock (TDHF) and the Matrix RPAE
.... 423
9.8
Examples of Application of the
RPA
Theory
..............430
9.8.1
The
RPA
With Separable Interactions
.............430
9.8.2
The RPAE for Metal Clusters
..................432
Contents xiii
9.9
The Adiabatic Time-Dependent LSDA (TDLSDA)
........... 438
9.9.1
The TDLSDA Longitudinal Response Function
....... 440
9.9.2
The TDLSDA Transverse Response Function
........ 445
9.10
RPA
and TDLSDA Commutators and Symmetry
Restoration
................................. 448
9.11
The Linear Response Based on the Green Functions; RPAE
...... 451
9.12
The Screened Response Function and the Dielectric Constant
..... 454
9.13
Examples of Application of the TDLSDA Theory
........... 456
9.13.1
Quantum Wells Under a Very High External Magnetic Field
456
9.13.2
Quantum Dots Under a Magnetic Field
............ 468
Chapter
10
Dynamic Correlations and the Response Function
491
10.1
Introduction
................................ 491
10.2
Interaction Energy and Correlation Energy
............... 491
10.3
The
RPA
Correlation Energy
....................... 494
10.3.1
The
RPA
Correlation Energy for the Cold and Dilute Gas
of Bosons and
Fermions
.................... 495
10.4
Theories Beyond the
RPA
........................ 497
10.5
The STLS Theory
............................. 500
10.6
Comparison of Different Theories for the Electron Gas in 2D
..... 502
10.7
Quasiparticle Properties
.......................... 504
10.8
Nonlocal Effects
.............................. 506
10.9
Mean Energy of Many-Particle Excitations
............... 515
10.10
The Polarization Potential Model
.................... 516
10.11
The Gross-Kohn Model
.......................... 519
10.12
The Method of
Lorentz
Transforms
................... 523
Chapter
11
The Hydrodynamic and Elastic Models
527
11.1
The Hydrodynamic Model for Bosons
.................. 527
11.1.1
Backflow
............................. 530
11.1.2
Compression and Surface Modes of Spherical Drops
..... 530
11.1.3
Compression and Surface Modes of
a Bose
Gas in a
Magnetic Trap
.......................... 534
11.1.4
Compression and Surface Modes of a Superfluid Trapped
Fermi Gas
............................ 535
11.1.5
The Moment of Inertia and the Scissor Mode of
a Bose
Gas
in a Magnetic Trap
....................... 536
11.1.6
Vortices in the
Bose
Gas in a Magnetic Trap
......... 541
11.2
The Fluidodynamic and Hydrodynamic Model for
Fermions
...... 544
11.2.1
Dipolar Modes in Metal Clusters
............... 552
11.2.2
Spin Oscillations in Trapped Fermi Gases
.......... 554
11.2.3
The Scalar Quadrupole Mode in Confined Systems
..... 554
11.2.4
The Scissor Mode in Fermi Systems
.............. 556
xiv Contents
11.2.5 The Moment
of Inertia of
Quantum
Dots
........... 558
11.2.6
The Vibrating Potential Model
................ 562
11.3
The Surface Vibrations of Charged Systems in 2D and
3D ...... 566
11.3.1
Surface Vibrations of Charged Metal Clusters
........ 567
11.3.2
Edge Vibrations of Quantum Dots
.............. 569
Index
576
|
| adam_txt |
Contents
Preface
v
Preface
to the Second Edition
vii
Chapter
1
The Independent-Particle Model
1
1.1
Introduction
. 1
1.2
Bosons
. 2
1.3
Fermions
. 3
1.4
Matrix Elements of One-Body Operators
. 6
1.5
Matrix Elements of Two-Body Operators
. 8
1.6
Density Matrices
. 10
1.7
The Ideal
Bose
Gas Confined in a Harmonic Potential
. 12
1.8
The Fermi Gas
. 14
1.8.1
Excited States
. 19
1.8.2
Polarized Fermi Gas
. 23
1.8.3
The Fermi Gas in Two Dimensions with Rashba Interaction
. 24
1.9
Finite Temperature and Quasiparticles
. 25
Chapter
2
The Hartree-Pock Theory
35
2.1
Introduction
. 35
2.2
The Hartree-Fock Method for
Fermions
. 36
2.2.1
Examples of Physical Systems Treated by the Hartree-Fock
Method
. 40
2.2.2
Examples of Infinite Systems Treated by the Hartree-Fock
Method
. 51
2.3
The Hartree-Fock Method for Bosons
. 55
2.4
The Gross-Pitaevskii Equations
. 56
2.5
Hartree-Fock in Second Quantization Language
. 58
2.6
Hartree-Fock at Finite Temperature
. 60
2.7
Hartree-Fock-Bogoliubov and BCS
. 65
2.8
Appendix: Second Quantization
. 69
x
Contents
Chapter
3
The Brueckner-Hartree-Fock Theory
76
3.1
Introduction
. 76
3.2
The Lippman-Schwinger Equation
. 76
3.3
The Bethe-Goldstone Equation
. 78
3.4
Examples of Application of the BHF Theory
. 80
3.4.1
The One-Dimensional Fermion System
. 80
3.4.2
Ultracold Highly Polarized Fermi Gases
. 81
3.5
Numerical Results of BHF Calculation in Different Systems
. 84
3.6
The
g
Matrix for the 2D Electron Gas
. 86
3.6.1
Decomposition in Partial Waves
. 87
3.6.2
The Separable Approximation
. 91
3.6.3
The
g
Matrix Expansion
. 95
3.6.4
Numerical Results and Discussion
. 98
3.7
The
g
Matrix for Confined Electron Systems
. 100
3.7.1
Effective Interaction in Confined Electron Systems
. 108
3.8
The BBP Method
. 110
3.8.1
Appendix
. 113
Chapter
4
The Density Functional Theory
116
4.1
Introduction
. 116
4.2
The Density Functional Formalism
. 116
4.3
Examples of Application of the Density Functional Theory
. 118
4.3.1
The Thomas-Fermi Theory for the Atom
. 118
4.3.2
The Gross-Pitaevskii Theory for the Ground State of a Dilute
Gas of Bosons
. 120
4.3.3
The Thomas Fermi Approximation for the Fermi Gas Confined
in a Harmonic Potential
. 121
4.4
The Kohn-Sham Equations
. 125
4.5
The Local Density Approximation for the Exchange-Correlation Energy
127
4.6
The Local Spin Density Approximation (LSDA)
. 128
4.7
Inclusion of Current Terms in the DFT (CDFT)
. 131
4.8
The Ensemble Density Functional Theory (EDFT)
. 134
4.9
The DFT for Strongly Correlated Systems: Nuclei and Helium
. 135
4.10
The DFT for Mixed Systems
. 145
4.11
Symmetries and Mean Field Theories
. 150
Chapter
5
The Confined 2D Electron Gas in a Magnetic Field
159
5.1
Introduction
. 159
5.2
Quantum Dots in a Magnetic Field
. 159
5.2.1
The
ω0
»
шс
Case
. 160
5.2.2
The
шс
>
ω0
Case
. 161
5.2.3
The Maximum Density Droplet
(MDD)
State
. 163
5.3
The Fractional Regime
. 165
Contents xi
5.4
The Hall Effect
. 167
5.5
Elliptical Quantum Dots
. 169
5.5.1
Analogies with the Bose-Einstein Condensate in a
Rotating Trap
. 173
5.6
The DFT for Quantum Dots in a Magnetic Field
. 175
5.7
Quantum Wires
. 189
5.8
The Aharanov-Bohm Effect and Quantum Rings
. 194
5.9
Quantum Molecules
. 200
5.9.1
The
В
= 0
Case
. 201
5.9.2
Β φ
0. 206
Chapter
6
Spin-Orbit Coupling in the Confined 2D Electron Gas
218
6.1
Spin-Orbit Coupling in Semiconductors
. 219
6.2
Spin-Orbit Effects on Single-Particle States in Quantum Wells
. 220
6.2.1
The Case in Which Either
Ад
= 0
or \D
= 0. 221
6.2.2
The General Case Where XR
φ
0
and \D
φ
0. 223
6.3
Single-Particle Level Transitions in Quantum Wells
. 227
6.4
The Magnetic Field in Plane
. 230
6.5
Spin-Orbit Effects on Single-Particle States in Quantum Dots
. 231
6.5.1
Single-Particle Transitions in Dots
. 237
6.6
Spin-Orbit Effects on Single-Particle States in Quantum Wires
. 241
6.7
The LSDA with Spin-Orbit Coupling
. 245
6.8
Comparison with Experiments in Quantum Wells
. 252
6.9
LSDA Results and Comparison with Experiments for Quantum Dots
. . 256
6.10
LSDA Results for Quantum Wires
. 271
6.11
Appendix A
. 280
6.12
Appendix
В
. 281
Chapter
7
Monte Carlo Methods
285
7.1
Introduction
. 285
7.2
Standard Quadrature Methods
. 285
7.3
Random Variable Distributions and the Central Limit Theorem
. 287
7.4
Sampling Techniques
. 289
7.4.1
The Inversion Rule
. 289
7.4.2
The Rejection Method
. 290
7.4.3
Markov Chains
. 290
7.5
The Metropolis Algorithm [M(RT)2}
. 294
7.6
Variational Monte Carlo for Liquid 4He
. 296
7.7
Variational Monte Carlo for
Fermions
. 298
7.8
Optimization of Variational Wave Functions
. 301
7.9
Monte Carlo Methods and Quantum Mechanics
. 304
7.10
Propagation of a State in Imaginary Time
. 305
7.11
The
Schrödinger
Equation in Imaginary Time
. 306
xii Contents
7.12
Importance
Sampling
. 308
7.13
Importance Sampling and Green Functions
. 311
7.14
Fermion Systems and the Sign Problem
. 313
7.15
Two Examples of DMC Calculations in Many-Body Systems
. 316
7.15.1
The Equation of State of Diluted Ultracold Fermi Gases in
the BEC-BCS Crossover
.316
7.15.2
Many-Nucleon Systems
.318
Chapter
8
The Linear Response Function Theory
325
8.1
Introduction
. 325
8.2
The General Formalism
. 328
8.3
The Linear Response Function and Sum Rules
. 332
8.4
Finite Temperature
. 336
8.5
The Density Response
. 338
8.6
The Density Response for Noninteracting Homogeneous Systems
. . . 342
8.7
The Current Response to an Electromagnetic Field
. 347
8.8
The Conductivity of Quantum Wires
. 352
8.9
Magnetoconductivity
. 360
8.9.1
The Kohn Theorem
. 360
8.9.2
Magnetoconductivity and the Quantum Hall Effect
. 363
8.10
The Larmor Theorem
. 367
8.10.1
Electron Spin Precession with Rashba Spin-Orbit Coupling
. 367
8.11
Deviations from Kohn and Larmor Theorems Due to
Spin-Orbit Coupling
. 369
8.11.1
Spin-Orbit Splitting of Cyclotron Resonance
. 369
8.11.2
Spin Splitting of Landau Levels
. 374
8.12
Spin-Hall Conductivity
. 375
8.12.1
The Spin-Hall Effect at a Finite Magnetic Field
. 377
8.12.2
Spin-Hall Conductivity Without SO Coupling
. 378
8.12.3
Influence of the SO Coupling on the Spin-Hall Conductivity
. 379
8.13
Hall Conductivity in Graphene
. 382
Chapter
9
The Linear Response Function in Different Models
387
9.1
The Linear Response Function in Landau Theory
.387
9.2
Time Dependent
Hartree
(TDH) for Homogeneous Systems: The
RPA
401
9.3
TDH for the Density Matrix and the Landau Equations
.405
9.4
The
RPA
for the Electron Gas in Different Dimensions: The Plasmon
407
9.5
The
RPA
for Bosons
.413
9.6
The Time-Dependent Gross-Pitaevskii Theory
.417
9.7
Time-Dependent Hartree^Fock (TDHF) and the Matrix RPAE
. 423
9.8
Examples of Application of the
RPA
Theory
.430
9.8.1
The
RPA
With Separable Interactions
.430
9.8.2
The RPAE for Metal Clusters
.432
Contents xiii
9.9
The Adiabatic Time-Dependent LSDA (TDLSDA)
. 438
9.9.1
The TDLSDA Longitudinal Response Function
. 440
9.9.2
The TDLSDA Transverse Response Function
. 445
9.10
RPA
and TDLSDA Commutators and Symmetry
Restoration
. 448
9.11
The Linear Response Based on the Green Functions; RPAE
. 451
9.12
The Screened Response Function and the Dielectric Constant
. 454
9.13
Examples of Application of the TDLSDA Theory
. 456
9.13.1
Quantum Wells Under a Very High External Magnetic Field
456
9.13.2
Quantum Dots Under a Magnetic Field
. 468
Chapter
10
Dynamic Correlations and the Response Function
491
10.1
Introduction
. 491
10.2
Interaction Energy and Correlation Energy
. 491
10.3
The
RPA
Correlation Energy
. 494
10.3.1
The
RPA
Correlation Energy for the Cold and Dilute Gas
of Bosons and
Fermions
. 495
10.4
Theories Beyond the
RPA
. 497
10.5
The STLS Theory
. 500
10.6
Comparison of Different Theories for the Electron Gas in 2D
. 502
10.7
Quasiparticle Properties
. 504
10.8
Nonlocal Effects
. 506
10.9
Mean Energy of Many-Particle Excitations
. 515
10.10
The Polarization Potential Model
. 516
10.11
The Gross-Kohn Model
. 519
10.12
The Method of
Lorentz
Transforms
. 523
Chapter
11
The Hydrodynamic and Elastic Models
527
11.1
The Hydrodynamic Model for Bosons
. 527
11.1.1
Backflow
. 530
11.1.2
Compression and Surface Modes of Spherical Drops
. 530
11.1.3
Compression and Surface Modes of
a Bose
Gas in a
Magnetic Trap
. 534
11.1.4
Compression and Surface Modes of a Superfluid Trapped
Fermi Gas
. 535
11.1.5
The Moment of Inertia and the Scissor Mode of
a Bose
Gas
in a Magnetic Trap
. 536
11.1.6
Vortices in the
Bose
Gas in a Magnetic Trap
. 541
11.2
The Fluidodynamic and Hydrodynamic Model for
Fermions
. 544
11.2.1
Dipolar Modes in Metal Clusters
. 552
11.2.2
Spin Oscillations in Trapped Fermi Gases
. 554
11.2.3
The Scalar Quadrupole Mode in Confined Systems
. 554
11.2.4
The Scissor Mode in Fermi Systems
. 556
xiv Contents
11.2.5 The Moment
of Inertia of
Quantum
Dots
. 558
11.2.6
The Vibrating Potential Model
. 562
11.3
The Surface Vibrations of Charged Systems in 2D and
3D . 566
11.3.1
Surface Vibrations of Charged Metal Clusters
. 567
11.3.2
Edge Vibrations of Quantum Dots
. 569
Index
576 |
| any_adam_object | 1 |
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| author | Lipparini, Enrico |
| author_GND | (DE-588)138257043 |
| author_facet | Lipparini, Enrico |
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| ctrlnum | (OCoLC)474501171 (DE-599)BVBBV023307751 |
| dewey-full | 530.144 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.144 |
| dewey-search | 530.144 |
| dewey-sort | 3530.144 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023307751 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:49:10Z |
| indexdate | 2024-07-09T21:15:30Z |
| institution | BVB |
| isbn | 9812709312 9789812709318 9789812709325 9812709320 |
| language | English |
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| physical | XIV, 582 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | World Scientific |
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| spelling | Lipparini, Enrico Verfasser (DE-588)138257043 aut Modern many-particle physics atomic gases, nanostructures and quantum liquids Enrico Lipparini 2. ed. New Jersey [u.a.] World Scientific 2008 XIV, 582 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Many-body problem Particles (Nuclear physics) Quantum theory Quantentheorie Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Vielteilchentheorie (DE-588)4331960-9 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016492085&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lipparini, Enrico Modern many-particle physics atomic gases, nanostructures and quantum liquids Many-body problem Particles (Nuclear physics) Quantum theory Quantentheorie Vielteilchentheorie (DE-588)4331960-9 gnd |
| subject_GND | (DE-588)4331960-9 (DE-588)4123623-3 |
| title | Modern many-particle physics atomic gases, nanostructures and quantum liquids |
| title_auth | Modern many-particle physics atomic gases, nanostructures and quantum liquids |
| title_exact_search | Modern many-particle physics atomic gases, nanostructures and quantum liquids |
| title_exact_search_txtP | Modern many-particle physics atomic gases, nanostructures and quantum liquids |
| title_full | Modern many-particle physics atomic gases, nanostructures and quantum liquids Enrico Lipparini |
| title_fullStr | Modern many-particle physics atomic gases, nanostructures and quantum liquids Enrico Lipparini |
| title_full_unstemmed | Modern many-particle physics atomic gases, nanostructures and quantum liquids Enrico Lipparini |
| title_short | Modern many-particle physics |
| title_sort | modern many particle physics atomic gases nanostructures and quantum liquids |
| title_sub | atomic gases, nanostructures and quantum liquids |
| topic | Many-body problem Particles (Nuclear physics) Quantum theory Quantentheorie Vielteilchentheorie (DE-588)4331960-9 gnd |
| topic_facet | Many-body problem Particles (Nuclear physics) Quantum theory Quantentheorie Vielteilchentheorie Lehrbuch |
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