Quantum hall effects: field theoretical approach and related topics
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| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2008
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXIV, 706 S. graph. Darst. |
| ISBN: | 9789812700322 9812700323 |
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| 020 | |a 9789812700322 |9 978-981-270-032-2 | ||
| 020 | |a 9812700323 |9 981-270-032-3 | ||
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| 084 | |a UP 5110 |0 (DE-625)146414: |2 rvk | ||
| 100 | 1 | |a Ezawa, Zyun F. |e Verfasser |0 (DE-588)1034893866 |4 aut | |
| 245 | 1 | 0 | |a Quantum hall effects |b field theoretical approach and related topics |c Zyun F. Ezawa |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2008 | |
| 300 | |a XXXIV, 706 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Quanten-Hall-Effekt |0 (DE-588)4124013-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quanten-Hall-Effekt |0 (DE-588)4124013-3 |D s |
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| adam_text | Contents
Preface vii
Part. I Quantum Field Theory
1
1.
Quantum Mechanics
3
1.1
Hubert Spaces
............................................. 3
1.2
Canonical Formalism
....................................... 4
1.3
Creation and Annihilation Operators
......................... 6
1.4
Uncertainty Principle
....................................... 10
1.5
Coherent States and
von
Neumann Lattice
.................... 11
1.6
Squeezed Coherent State
.................................... 14
1.7
Particle Number and Phase
................................. 16
1.8
Macroscopic Coherence
..................................... 18
2.
Quantum Field Theory
20
2.1
One-Body Hamiltonian
..................................... 20
2.2
Many-Body Hamiltonian
................................... 21
2.3
Boson Field Operators
...................................... 23
2.4
Quantum Field Theory
..................................... 25
2.5
Fermion Field Operators
.................................... 27
2.6
Electrons Interacting with Electromagnetic Field
............... 29
3.
Canonical Quantization
31
3.1
Relativistic Particles and Waves
.............................. 31
3.2 Schrödinger
Field
.......................................... 32
3.3
Real Klein-Gordon Field
.................................... 37
3.4
Complex Klein-Gordon Field
................................ 42
CONTENTS
3.5 Nöther
Currents...........................................
44
4.
Spontaneous Symmetry Breaking
47
4.1
Ferromagnets
............................................. 47
4.2
Real Klein-Gordon Field
.................................... 51
4.3
Complex Klein-Gordon Field
................................ 55
4.4
Sigma Model
.............................................. 56
4.5 Schrödinger
Field
.......................................... 58
4.6
Superfluidity
.............................................. 62
4.7 Goldstone
Theorem
........................................ 64
5.
Electromagnetic Field
67
5.1
Maxwell Equations
........................................ 67
5.2
Canonical Quantization
.................................... 70
5.3
Interaction with Matter Field
................................ 77
5.4
Anderson-Higgs Mechanism
................................ 79
5.5
Massive Vector Field
....................................... 81
5.6
Superconductivity
......................................... 83
5.7
Aharonov-Bohm Effect
..................................... 89
6.
Dirac Field
94
6.1
Dirac Equation
............................................ 94
6.2
Plane Wave Solutions
...................................... 97
6.3
Canonical Quantization
.................................... 99
6.4
Interaction with Electromagnetic Field
........................ 103
6.5
Weyl Field (Massless Dirac Field)
............................ 105
6.6
Dirac Electrons in Magnetic Field
............................ 108
7.
Topological
Solitons 113
7.1
Topological Sectors
........................................ 113
7.2
Classical Fields
............................................ 115
7.3
Solitary Waves, Kinks and
Solitons........................... 117
7.4
Sine-Gordon
Solitons....................................... 119
7.5
Vortex
Solitons............................................ 123
7.6
Homotopy Classes
......................................... 127
7.7
O(3) Skyrmions
............................................ 132
7.8
CP^ 1 Skyrmions
.......................................... 138
8.
Anyons
144
8.1
Spin and Statistics
......................................... 144
8.2
Fractional Statistics
........................................ 148
8.3
Quantum Mechanics
....................................... 150
CONTENTS
8.4 Chern-Simons
Gauge Theory
................................ 153
8.5
Anyon Field Operators
..................................... 157
Part. II Monolayer Quantum Hall Systems
161
9.
Overview of Monolayer QH Systems
163
10.
Landau Quantization
177
10.1
Planar Electrons
........................................... 177
10.2
Cyclotron Motion
.......................................... 181
10.3
Symmetric Gauge
.......................................... 187
10.4
Landau Gauge
............................................ 190
10.5 von
Neumann Lattice
...................................... 193
10.6
Electrons in Nth Landau Level
............................... 195
10.7
Hall Current
.............................................. 199
11.
Quantum Hall Effects
204
11.1
Incompressibility
.......................................... 204
11.2
Integer Quantum Hall Effects
............................... 205
11.3
Fractional Quantum Hall Effects
............................. 207
11.4
Quasiparticles
............................................. 210
11.5
Hall Plateaux
.............................................. 213
12.
Quasiparticles and Activation Energy
215
12.1
Impurity Potentials
........................................ 215
12.2
Gap Energies
.............................................. 216
12.3
Dispersion Relation
........................................ 219
12.4
Thermal Activation
........................................ 222
13.
Field Theory of Composite Particles
227
13.1
Composite Particles
........................................ 227
13.2
Statistical Transmutation
.................................... 230
13.3
Effective Magnetic Field
.................................... 233
13.4
Dressed Composite Particles
................................ 235
13.5
Composite Particles in Lowest Landau Level
.................. 239
13.6
Composite
Fermions
in Lowest Landau Level
................. 242
14.
Composite Bosons and Semiclassical Analysis
246
14.1
Ground State and Laughlin Wave Function
.................... 246
CONTENTS
14.2 Perturbative
Excitations....................................
248
14.3
Vortex Excitations
.......................................... 250
14.4
Field Theory of Vortex
Solitons.............................. 255
14.5
Haldane-Halperin Hierarchy
................................ 258
15.
Quantum Hall Ferromagnets
261
15.1
Spin Coherence
............................................ 261
15.2
Spin Degree of Freedom
.................................... 263
15.3
Composite Bosons and Spin-Charge Separation
................ 265
15.4
Spin Field, Sigma Field and CP1 Field
........................ 268
15.5
Effective Hamiitonian
...................................... 271
16.
Spin Textures
274
16.1
Spin Excitations
........................................... 274
16.2
Factorizable Skyrmions
..................................... 277
16.3
Skyrmion Excitation Energy
................................. 284
16.4
Experimental Evidence
..................................... 287
17.
Hierarchy of Fractional QH States
291
17.1
Jain Hierarchy
............................................. 291
17.2
Landau Levels of Composite
Fermions
....................... 294
17.3
Beyond Principal Sequences
................................. 296
17.4
Spin Polarization
.......................................... 298
17.5
Gap Energies
.............................................. 301
18.
Edge Effects
307
18.1
Edge Currents and Bulk Currents
............................ 307
18.2
Shot Noises of Fractional Charges
............................ 308
18.3
Chiral Edge Excitations
..................................... 311
18.4
Chiral Tomonaga-Luttinger Liquid
........................... 312
18.5
Electrodynamics on Edge
................................... 316
18.6
Edge Tunneling and Sine-Gordon
Solitons.................... 320
19.
Stripes and Bubbles in Higher Landau Levels
325
19.1
Higher Landau Levels
...................................... 325
19.2
Haldane s Pseudopotentials
................................. 327
19.3
Effective Coulomb Interactions
.............................. 328
19.4
Density Matrix Renormalization Group Method
............... 331
19.5
Stripes, Bubbles and Wigner Crystal
.......................... 332
20.
Quantum Hall Effects in Graphene
335
20.1
Unconventional QH Effects
................................. 335
CONTENTS
20.2 Graphene and Dirac
Electrons
............................... 338
20.3 Dirac Hamiltonian and Supersymmetry...................... 343
20.4
Effective
Coulomb
Interactions
.............................. 346
20.5 Excitonic
Condensation
..................................... 352
20.6 Valley
Polarization
......................................... 355
20.7
Multilayer
Graphene Systems............................... 360
20.8
Berry
Phase and Index Theorem............................. 365
Part.
III
Bilayer Quantum Hall Systems 367
21.
Overview of
Bilayer QH Systems 369
22. SU(2) Pseudospin
Structure
383
22.1 Bilayer
Planar Electrons ....................................
383
22.2 Pseudospins.............................................. 385
22.3
Tunneling Interaction
...................................... 387
22.4
unbalanced Configuration
.................................. 388
22.5
Capacitance Energy
........................................ 392
22.6
Compound States
.......................................... 393
22.7
Charge-Transferable States
.................................. 394
23.
Bilayer-Locked States
400
23.1
Composite-Boson Field
..................................... 400
23.2
Wave Functions
........................................... 404
23.3
Ground State
.............................................. 405
23.4
Vortex Excitations
.......................................... 406
24.
Interlayer Coherence
409
24.1
Pseudospin Ferromagnet
................................... 409
24.2
Effective Hamiltonian
...................................... 413
24.3
Pseudospin Waves
......................................... 415
24.4
Anomalous Bilayer QH Currents
............................ 417
24.5
Pseudospin Texture
........................................ 424
25.
SU(4) Quantum Hall Ferromagnets
428
25.1
SU(4) Isospin Structure
..................................... 428
25.2
SU(4) Isospin Fields
........................................ 431
25.3
SU(4) Isospin Waves
....................................... 433
25.4
SU(4) Isospin Textures
...................................... 436
CONTENTS
25.5
Excitation
Energy
of
SU(4)
Skyrmions
........................ 440
25.6
Activation Energy Anomaly
................................. 446
26.
Bilayer Quantum Hall Systems at
v
= 2 454
26.1
Spin Phase, Ppin Phase and Canted Phase
..................... 454
26.2
Ground-State Energy
....................................... 457
26.3
Ground-State Structure
..................................... 460
26.4
Phase Diagrams
........................................... 463
26.5
Experimental Data
......................................... 466
26.6
SU(4) Breaking and Grassmannian Fields
..................... 471
26.7
Grassmannian G^z
Solitons................................. 475
26.8
Genuine Bilayer versus Two-Monolayer Systems
............... 479
26.9
Experimental Indication of Biskyrmions
...................... 482
27.
Bilayer Quantum-Hall Junction
485
27.1
Josephson-Like
Phenomena
................................. 485
27.2
Parallel Magnetic Field
..................................... 487
27.3
Effective Hamiltonian
...................................... 493
27.4
Commensurate-Incommensurate Phase Transition
............. 495
27.5
Soliton Lattice
............................................. 499
27.6
Anomalous Diagonal Resistivity
............................. 508
27.7
Plasmon Excitations
........................................ 514
27.8
Josephson-Like
Effects
...................................... 516
Part. IV Microscopic Theory
521
28.
Overview of Microscopic Theory
523
29.
Noncommutative Geometry
534
29.1
Noncommutative Coordinate
............................... 534
29.2
Weyl Operator and Symbol
................................. 535
29.3
Magnetic Translation
....................................... 541
29.4
Density Operators
......................................... 543
29.5 SU(N)-Extended W„
Algebra
............................... 549
29.6
Classical Fields
............................................ 552
29.7
Topological Charge Density
................................. 557
29.8
Кас
-Moody Algebra on Edges
............................... 559
30.
Landau Level Projection
562
CONTENTS
30.1
Projected
Coulomb
Interactions
.............................. 562
30.2 Monolayer QH System..................................... 565
30.3
Electron-Hole Pair Excitations
............................... 569
30.4 Electron
Excitation and Hole Excitation
....................... 570
30.5
Bilayer System without Spin (v
= 1).......................... 573
30.6
Bilayer System with Spin (v
= 1)............................. 575
30.7
Bilayer System with Spins (v
= 2)............................ 578
31.
Noncommutative
Solitons 584
31.1
Topological Charge and Electric Charge
...................... 584
31.2
Microscopic Skyrmion States
................................ 585
31.3
Noncommutative
CP1
Skyrmion
............................. 589
31.4
Hole and Skyrmion
........................................ 592
31.5
Skyrmion Wave Functions
.................................. 593
31.6
Hardcore Interaction
....................................... 595
31.7
Coulomb Interaction
....................................... 600
31.8
SU(4) Skyrmions
........................................... 605
32.
Exchange Interactions and Effective Theory
607
32.1
Exchange Hamiltonian
..................................... 607
32.2
Decomposition Formula
.................................... 612
32.3
Spontaneous Symmetry Breaking
............................ 615
32.4
Classical Equations of Motion
............................... 616
32.5
Four-Layer Condenser Model
............................... 618
32.6
Derivative Expansion and Effective Theory
................... 622
32.7
Noncommutative
CP^ 1 Model
............................. 627
32.8
Equations of Motion and Hall Currents
....................... 631
32.9
Hall Currents in Pseudospin QH Ferromagnet
................. 634
Appendices
643
A Energy Scales
............................................. 643
В
Hausdorff Formulas
....................................... 645
С
Group SU(2) and
Pauli
Matrices
............................. 647
D
Groups SU(N) and SU(2N)
.................................. 647
E
Cauchy-Riemann Equations
................................. 650
F
Green Function
............................................ 651
G Bogoliubov
Transformation
................................. 652
H
Energy-Momentum Tensor
.................................. 654
I Exchange Interaction
....................................... 655
J
Mermin-Wagner Theorem
.................................. 659
K Lorentz
Transformation
..................................... 663
L
One-Dimensional
Soliton
Solutions
.......................... 666
CONTENTS
M
Field-Theoretical Vortex Operators
........................... 669
N
Bosonization in One-Dimensional Space
...................... 672
О
Coulomb Energy Formulas
.................................. 677
Ρ
W«,
Algebra
............................................... 679
References
681
Index
699
|
| adam_txt |
Contents
Preface vii
Part. I Quantum Field Theory
1
1.
Quantum Mechanics
3
1.1
Hubert Spaces
. 3
1.2
Canonical Formalism
. 4
1.3
Creation and Annihilation Operators
. 6
1.4
Uncertainty Principle
. 10
1.5
Coherent States and
von
Neumann Lattice
. 11
1.6
Squeezed Coherent State
. 14
1.7
Particle Number and Phase
. 16
1.8
Macroscopic Coherence
. 18
2.
Quantum Field Theory
20
2.1
One-Body Hamiltonian
. 20
2.2
Many-Body Hamiltonian
. 21
2.3
Boson Field Operators
. 23
2.4
Quantum Field Theory
. 25
2.5
Fermion Field Operators
. 27
2.6
Electrons Interacting with Electromagnetic Field
. 29
3.
Canonical Quantization
31
3.1
Relativistic Particles and Waves
. 31
3.2 Schrödinger
Field
. 32
3.3
Real Klein-Gordon Field
. 37
3.4
Complex Klein-Gordon Field
. 42
CONTENTS
3.5 Nöther
Currents.
44
4.
Spontaneous Symmetry Breaking
47
4.1
Ferromagnets
. 47
4.2
Real Klein-Gordon Field
. 51
4.3
Complex Klein-Gordon Field
. 55
4.4
Sigma Model
. 56
4.5 Schrödinger
Field
. 58
4.6
Superfluidity
. 62
4.7 Goldstone
Theorem
. 64
5.
Electromagnetic Field
67
5.1
Maxwell Equations
. 67
5.2
Canonical Quantization
. 70
5.3
Interaction with Matter Field
. 77
5.4
Anderson-Higgs Mechanism
. 79
5.5
Massive Vector Field
. 81
5.6
Superconductivity
. 83
5.7
Aharonov-Bohm Effect
. 89
6.
Dirac Field
94
6.1
Dirac Equation
. 94
6.2
Plane Wave Solutions
. 97
6.3
Canonical Quantization
. 99
6.4
Interaction with Electromagnetic Field
. 103
6.5
Weyl Field (Massless Dirac Field)
. 105
6.6
Dirac Electrons in Magnetic Field
. 108
7.
Topological
Solitons 113
7.1
Topological Sectors
. 113
7.2
Classical Fields
. 115
7.3
Solitary Waves, Kinks and
Solitons. 117
7.4
Sine-Gordon
Solitons. 119
7.5
Vortex
Solitons. 123
7.6
Homotopy Classes
. 127
7.7
O(3) Skyrmions
. 132
7.8
CP^"1 Skyrmions
. 138
8.
Anyons
144
8.1
Spin and Statistics
. 144
8.2
Fractional Statistics
. 148
8.3
Quantum Mechanics
. 150
CONTENTS
8.4 Chern-Simons
Gauge Theory
. 153
8.5
Anyon Field Operators
. 157
Part. II Monolayer Quantum Hall Systems
161
9.
Overview of Monolayer QH Systems
163
10.
Landau Quantization
177
10.1
Planar Electrons
. 177
10.2
Cyclotron Motion
. 181
10.3
Symmetric Gauge
. 187
10.4
Landau Gauge
. 190
10.5 von
Neumann Lattice
. 193
10.6
Electrons in Nth Landau Level
. 195
10.7
Hall Current
. 199
11.
Quantum Hall Effects
204
11.1
Incompressibility
. 204
11.2
Integer Quantum Hall Effects
. 205
11.3
Fractional Quantum Hall Effects
. 207
11.4
Quasiparticles
. 210
11.5
Hall Plateaux
. 213
12.
Quasiparticles and Activation Energy
215
12.1
Impurity Potentials
. 215
12.2
Gap Energies
. 216
12.3
Dispersion Relation
. 219
12.4
Thermal Activation
. 222
13.
Field Theory of Composite Particles
227
13.1
Composite Particles
. 227
13.2
Statistical Transmutation
. 230
13.3
Effective Magnetic Field
. 233
13.4
Dressed Composite Particles
. 235
13.5
Composite Particles in Lowest Landau Level
. 239
13.6
Composite
Fermions
in Lowest Landau Level
. 242
14.
Composite Bosons and Semiclassical Analysis
246
14.1
Ground State and Laughlin Wave Function
. 246
CONTENTS
14.2 Perturbative
Excitations.
248
14.3
Vortex Excitations
. 250
14.4
Field Theory of Vortex
Solitons. 255
14.5
Haldane-Halperin Hierarchy
. 258
15.
Quantum Hall Ferromagnets
261
15.1
Spin Coherence
. 261
15.2
Spin Degree of Freedom
. 263
15.3
Composite Bosons and Spin-Charge Separation
. 265
15.4
Spin Field, Sigma Field and CP1 Field
. 268
15.5
Effective Hamiitonian
. 271
16.
Spin Textures
274
16.1
Spin Excitations
. 274
16.2
Factorizable Skyrmions
. 277
16.3
Skyrmion Excitation Energy
. 284
16.4
Experimental Evidence
. 287
17.
Hierarchy of Fractional QH States
291
17.1
Jain Hierarchy
. 291
17.2
Landau Levels of Composite
Fermions
. 294
17.3
Beyond Principal Sequences
. 296
17.4
Spin Polarization
. 298
17.5
Gap Energies
. 301
18.
Edge Effects
307
18.1
Edge Currents and Bulk Currents
. 307
18.2
Shot Noises of Fractional Charges
. 308
18.3
Chiral Edge Excitations
. 311
18.4
Chiral Tomonaga-Luttinger Liquid
. 312
18.5
Electrodynamics on Edge
. 316
18.6
Edge Tunneling and Sine-Gordon
Solitons. 320
19.
Stripes and Bubbles in Higher Landau Levels
325
19.1
Higher Landau Levels
. 325
19.2
Haldane's Pseudopotentials
. 327
19.3
Effective Coulomb Interactions
. 328
19.4
Density Matrix Renormalization Group Method
. 331
19.5
Stripes, Bubbles and Wigner Crystal
. 332
20.
Quantum Hall Effects in Graphene
335
20.1
Unconventional QH Effects
. 335
CONTENTS
20.2 Graphene and Dirac
Electrons
. 338
20.3 Dirac Hamiltonian and Supersymmetry. 343
20.4
Effective
Coulomb
Interactions
. 346
20.5 Excitonic
Condensation
. 352
20.6 Valley
Polarization
. 355
20.7
Multilayer
Graphene Systems. 360
20.8
Berry
Phase and Index Theorem. 365
Part.
III
Bilayer Quantum Hall Systems 367
21.
Overview of
Bilayer QH Systems 369
22. SU(2) Pseudospin
Structure
383
22.1 Bilayer
Planar Electrons .
383
22.2 Pseudospins. 385
22.3
Tunneling Interaction
. 387
22.4
unbalanced Configuration
. 388
22.5
Capacitance Energy
. 392
22.6
Compound States
. 393
22.7
Charge-Transferable States
. 394
23.
Bilayer-Locked States
400
23.1
Composite-Boson Field
. 400
23.2
Wave Functions
. 404
23.3
Ground State
. 405
23.4
Vortex Excitations
. 406
24.
Interlayer Coherence
409
24.1
Pseudospin Ferromagnet
. 409
24.2
Effective Hamiltonian
. 413
24.3
Pseudospin Waves
. 415
24.4
Anomalous Bilayer QH Currents
. 417
24.5
Pseudospin Texture
. 424
25.
SU(4) Quantum Hall Ferromagnets
428
25.1
SU(4) Isospin Structure
. 428
25.2
SU(4) Isospin Fields
. 431
25.3
SU(4) Isospin Waves
. 433
25.4
SU(4) Isospin Textures
. 436
CONTENTS
25.5
Excitation
Energy
of
SU(4)
Skyrmions
. 440
25.6
Activation Energy Anomaly
. 446
26.
Bilayer Quantum Hall Systems at
v
= 2 454
26.1
Spin Phase, Ppin Phase and Canted Phase
. 454
26.2
Ground-State Energy
. 457
26.3
Ground-State Structure
. 460
26.4
Phase Diagrams
. 463
26.5
Experimental Data
. 466
26.6
SU(4) Breaking and Grassmannian Fields
. 471
26.7
Grassmannian G^z
Solitons. 475
26.8
Genuine Bilayer versus Two-Monolayer Systems
. 479
26.9
Experimental Indication of Biskyrmions
. 482
27.
Bilayer Quantum-Hall Junction
485
27.1
Josephson-Like
Phenomena
. 485
27.2
Parallel Magnetic Field
. 487
27.3
Effective Hamiltonian
. 493
27.4
Commensurate-Incommensurate Phase Transition
. 495
27.5
Soliton Lattice
. 499
27.6
Anomalous Diagonal Resistivity
. 508
27.7
Plasmon Excitations
. 514
27.8
Josephson-Like
Effects
. 516
Part. IV Microscopic Theory
521
28.
Overview of Microscopic Theory
523
29.
Noncommutative Geometry
534
29.1
Noncommutative Coordinate
. 534
29.2
Weyl Operator and Symbol
. 535
29.3
Magnetic Translation
. 541
29.4
Density Operators
. 543
29.5 SU(N)-Extended W„
Algebra
. 549
29.6
Classical Fields
. 552
29.7
Topological Charge Density
. 557
29.8
Кас
-Moody Algebra on Edges
. 559
30.
Landau Level Projection
562
CONTENTS
30.1
Projected
Coulomb
Interactions
. 562
30.2 Monolayer QH System. 565
30.3
Electron-Hole Pair Excitations
. 569
30.4 Electron
Excitation and Hole Excitation
. 570
30.5
Bilayer System without Spin (v
= 1). 573
30.6
Bilayer System with Spin (v
= 1). 575
30.7
Bilayer System with Spins (v
= 2). 578
31.
Noncommutative
Solitons 584
31.1
Topological Charge and Electric Charge
. 584
31.2
Microscopic Skyrmion States
. 585
31.3
Noncommutative
CP1
Skyrmion
. 589
31.4
Hole and Skyrmion
. 592
31.5
Skyrmion Wave Functions
. 593
31.6
Hardcore Interaction
. 595
31.7
Coulomb Interaction
. 600
31.8
SU(4) Skyrmions
. 605
32.
Exchange Interactions and Effective Theory
607
32.1
Exchange Hamiltonian
. 607
32.2
Decomposition Formula
. 612
32.3
Spontaneous Symmetry Breaking
. 615
32.4
Classical Equations of Motion
. 616
32.5
Four-Layer Condenser Model
. 618
32.6
Derivative Expansion and Effective Theory
. 622
32.7
Noncommutative
CP^"1 Model
. 627
32.8
Equations of Motion and Hall Currents
. 631
32.9
Hall Currents in Pseudospin QH Ferromagnet
. 634
Appendices
643
A Energy Scales
. 643
В
Hausdorff Formulas
. 645
С
Group SU(2) and
Pauli
Matrices
. 647
D
Groups SU(N) and SU(2N)
. 647
E
Cauchy-Riemann Equations
. 650
F
Green Function
. 651
G Bogoliubov
Transformation
. 652
H
Energy-Momentum Tensor
. 654
I Exchange Interaction
. 655
J
Mermin-Wagner Theorem
. 659
K Lorentz
Transformation
. 663
L
One-Dimensional
Soliton
Solutions
. 666
CONTENTS
M
Field-Theoretical Vortex Operators
. 669
N
Bosonization in One-Dimensional Space
. 672
О
Coulomb Energy Formulas
. 677
Ρ
W«,
Algebra
. 679
References
681
Index
699 |
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| author | Ezawa, Zyun F. |
| author_GND | (DE-588)1034893866 |
| author_facet | Ezawa, Zyun F. |
| author_role | aut |
| author_sort | Ezawa, Zyun F. |
| author_variant | z f e zf zfe |
| building | Verbundindex |
| bvnumber | BV023286265 |
| classification_rvk | UP 5110 |
| ctrlnum | (OCoLC)255922048 (DE-599)BVBBV023286265 |
| dewey-full | 537.6226 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 537 - Electricity and electronics |
| dewey-raw | 537.6226 |
| dewey-search | 537.6226 |
| dewey-sort | 3537.6226 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023286265 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:41:39Z |
| indexdate | 2024-07-09T21:14:59Z |
| institution | BVB |
| isbn | 9789812700322 9812700323 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016470962 |
| oclc_num | 255922048 |
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| owner_facet | DE-355 DE-BY-UBR DE-20 DE-384 DE-11 DE-188 |
| physical | XXXIV, 706 S. graph. Darst. |
| publishDate | 2008 |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Ezawa, Zyun F. Verfasser (DE-588)1034893866 aut Quantum hall effects field theoretical approach and related topics Zyun F. Ezawa 2. ed. New Jersey [u.a.] World Scientific 2008 XXXIV, 706 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quanten-Hall-Effekt (DE-588)4124013-3 gnd rswk-swf Quanten-Hall-Effekt (DE-588)4124013-3 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016470962&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ezawa, Zyun F. Quantum hall effects field theoretical approach and related topics Quanten-Hall-Effekt (DE-588)4124013-3 gnd |
| subject_GND | (DE-588)4124013-3 |
| title | Quantum hall effects field theoretical approach and related topics |
| title_auth | Quantum hall effects field theoretical approach and related topics |
| title_exact_search | Quantum hall effects field theoretical approach and related topics |
| title_exact_search_txtP | Quantum hall effects field theoretical approach and related topics |
| title_full | Quantum hall effects field theoretical approach and related topics Zyun F. Ezawa |
| title_fullStr | Quantum hall effects field theoretical approach and related topics Zyun F. Ezawa |
| title_full_unstemmed | Quantum hall effects field theoretical approach and related topics Zyun F. Ezawa |
| title_short | Quantum hall effects |
| title_sort | quantum hall effects field theoretical approach and related topics |
| title_sub | field theoretical approach and related topics |
| topic | Quanten-Hall-Effekt (DE-588)4124013-3 gnd |
| topic_facet | Quanten-Hall-Effekt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016470962&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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