Topology in condensed matter:
This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as th...
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|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Schriftenreihe: | Springer series in solid-state sciences
150 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form. TOC:Introduction.- Phason Dynamics in Aperiodic Crystals.- Defects, Surface Anchoring and Three-Dimensional Director Fields in the Lamellar Structure of Cholesteric Liquid Crystals.- Topology, Quasiperiodic Functions and the Transport Phenomena.- Topology in the Electron Theory of Metals.- Topological Defects in Carbon Nanocrystals.- Physics from Topology and Structures.- Two and Three Qubits Geometry and Hopf Fibrations.- Hamiltonian Monodromy as Lattice Defect.- Topology of Glasses |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIV, 254 S. Ill., graph. Darst. |
| ISBN: | 9783540234067 3540234063 |
Internformat
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| 020 | |a 3540234063 |c Pp. : EUR 128.35 (freier Pr.), ca. sfr 169.00 (freier Pr.) |9 3-540-23406-3 | ||
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| 245 | 1 | 0 | |a Topology in condensed matter |c M. I. Monastyrsky (ed.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a XIV, 254 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in solid-state sciences |v 150 | |
| 500 | |a Literaturangaben | ||
| 520 | |a This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form. TOC:Introduction.- Phason Dynamics in Aperiodic Crystals.- Defects, Surface Anchoring and Three-Dimensional Director Fields in the Lamellar Structure of Cholesteric Liquid Crystals.- Topology, Quasiperiodic Functions and the Transport Phenomena.- Topology in the Electron Theory of Metals.- Topological Defects in Carbon Nanocrystals.- Physics from Topology and Structures.- Two and Three Qubits Geometry and Hopf Fibrations.- Hamiltonian Monodromy as Lattice Defect.- Topology of Glasses | ||
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| 650 | 0 | 7 | |a Topologische Methode |0 (DE-588)4312758-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kondensierte Materie |0 (DE-588)4132810-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kondensierte Materie |0 (DE-588)4132810-3 |D s |
| 689 | 0 | 1 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 0 | 2 | |a Topologische Methode |0 (DE-588)4312758-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Monastyrskij, Michail I. |d 1945- |0 (DE-588)121283623 |4 edt | |
| 830 | 0 | |a Springer series in solid-state sciences |v 150 |w (DE-604)BV000016582 |9 150 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-014649659 | ||
Datensatz im Suchindex
| _version_ | 1804135142068846592 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION
M.
MONASTYRSKY
.................................................
1
1
TOPOLOGY
IN
THE
ELECTRON
THEORY
OF
METALS
A.M.
KOSEVICH
...................................................
3
1.1
INTRODUCTION
.................................................
3
1.2
DYNAMICS
OF
CONDUCTIVITY
ELECTRONS
AND
THE
FERMI
SURFACE
........
4
1.3
GEOMETRY
OF
THE
FERMI
SURFACE
IN
CRYSTAL
.......................
8
1.4
QUANTUM
MAGNETIC
OSCILLATIONS
AND
THE
SHAPE
OF
THE
FERMI
SURFACE
11
1.5
MAGNETICBREAKDOWN
.........................................
16
1.6
BAND
ELECTRONS
IN
THE
ELECTRIC
FIELD
AND
BLOCH
OSCILLATIONS
........
17
1.7
TOPOLOGY
OF
THE
FERMI
SURFACES
AND
LOW-TEMPERATURE
MAGNETORESISTIVITY
OF
METALS
...................................
19
1.8
BERRY S
PHASE
AND
THE
TOPOLOGY
OF
THE
ELECTRON
TRAJECTORIES
IN
THE
MAGNETICFIELD...............................................
23
REFERENCES
......................................................
28
2
TOPOLOGY,
QUASIPERIODIC
FUNCTIONS,
AND
THE
TRANSPORT
PHENOMENA
A.YA.
MALTSEV
AND
S.P.
NOVIKOV
...................................
31
2.1
INTRODUCTION
.................................................
31
2.1.1GALVANOMAGNETIC
PHENOMENA
IN
NORMAL
METALS:
CLASSICAL
RESULTS,
GSMF
LIMIT
....................................
31
2.1.2MODERN
IDEAS:
THE
GSMF
LIMIT,
TOPOLOGY,
AND
DYNAMICAL
SYSTEMS
................................................
36
2.1.3TRANSPORT
IN
2D
ELECTRON
GAS
AND
TOPOLOGY
OF
QUASIPERIODIC
FUNCTIONS...............................................
39
2.2
THECLASSIFICATIONOFFERMISURFACESANDTHE TOPOLOGICALQUANTUM
NUMBERS ...................................................
41
VIII
CONTENTS
2.3
QUASIPERIODICMODULATIONSOF2DELECTRONGASANDTHEGENERALIZED
NOVIKOVPROBLEM.............................................
49
REFERENCES
......................................................
58
3
THE
ROLE
OF
TOPOLOGY
IN
GROWTH
AND
AGGLOMERATION
R.
KERNER
.......................................................
61
3.1
INTRODUCTION
.................................................
61
3.2
TOPOLOGY
AND
GEOMETRY
OF
POLYGON
TILINGS
AND
NETWORKS
.........
62
3.3
DYNAMICAL
MODEL
OF
POLYGON
AGGLOMERATION
IN
TWO
DIMENSIONS
...
69
3.4
APPLICATION:
HOW
THE
FULLERENE
MOLECULES
ARE
FORMED.............
74
3.5
ONION
FULLERENES
AND
CARBON
TUBES
............................
79
3.6
RIGIDITY
AND
LOCAL
STRUCTURE
IN
COVALENT
GLASSES
.................
85
REFERENCES
......................................................
90
4
TOPOLOGICAL
DEFECTS
IN
CARBON
NANOCRYSTALS
V.A.
OSIPOV
.....................................................
93
4.1
INTRODUCTION
.................................................
93
4.2
GEOMETRY
AND
TOPOLOGY
OF
CARBON
NANOPARTICLES.................
94
4.3
ELECTRONICPROPERTIES
.........................................
98
4.3.1THEORY:
BASIC
ASSUMPTIONS
...............................
99
4.4
SPHERICAL
MOLECULES...........................................102
4.4.1THE
MODEL..............................................102
4.4.2EXTENDED
ELECTRON
STATES
.................................104
4.4.3NUMERICAL
RESULTS
.......................................105
4.4.4ZERO-ENERGY
MODES
......................................106
4.5
NANOCONES...................................................107
4.5.1THE
MODEL..............................................107
4.5.2ELECTRON
STATES
..........................................108
4.5.3NUMERICAL
RESULTS
.......................................110
4.6
HYPERBOLOID
GEOMETRY........................................110
4.6.1THE
MODEL..............................................110
4.6.2ELECTRON
STATES
..........................................111
4.6.3NUMERICAL
RESULTS
.......................................113
4.7
CONCLUSIONS..................................................114
REFERENCES
......................................................115
5
PHYSICS
FROM
TOPOLOGY
AND
STRUCTURES
J.
YI
...........................................................
117
5.1
INTRODUCTION
.................................................117
5.2
QUANTUMHALLEFFECT..........................................118
5.3
SHAPIRO
STEPS
IN
JOSEPHSON
JUNCTIONS
...........................122
5.4
CHARGEDENSITYWAVES
........................................126
5.5
QUANTUMPHASES.............................................129
5.6
CARBONNANOTUBES
...........................................132
CONTENTS
IX
5.7
CONCLUSIONS..................................................136
REFERENCES
......................................................136
6
PHASON
DYNAMICS
IN
APERIODIC
CRYSTALS
T.
JANNSEN
.....................................................
139
6.1
INTRODUCTION
.................................................139
6.1.1QUASIPERIODIC
CRYSTALS
...................................139
6.1.2EXAMPLES
OF
QUASIPERIODIC
CRYSTALS
........................140
6.1.3SYMMETRY
..............................................141
6.2
EMBEDDING
IN
SUPERSPACE
.....................................143
6.3
SIMPLE
MODELS
FOR
INCOMMENSURATE
STRUCTURES
...................145
6.3.1DISPLACIVELY
MODULATED
PHASES
............................145
6.3.2THE
DOUBLE-CHAIN
MODEL
FOR
INCOMMENSURATE
COMPOSITES
....147
6.3.3THE
GROUND
STATE
OF
THE
DCM
............................147
6.4
PHONONSANDPHASONS.........................................148
6.4.1PHONONS
IN
APERIODIC
CRYSTALS
............................148
6.4.2PHASON
EXCITATIONS
......................................151
6.4.3THE
PHASON
CONTENT
OF
PHONONS...........................153
6.5
NONLINEAR
PHASON
DYNAMICS
...................................154
6.5.1MODULATED
PHASES
.......................................154
6.5.2INCOMMENSURATE
COMPOSITES
..............................155
6.6
SLIDING
ON
A
QUASIPERIODIC
SUBSTRATE............................160
6.6.1A
MODEL................................................160
6.6.2NONLINEAR
DYNAMICS
AND
FRICTION
..........................162
6.7
CONCLUSIONS..................................................162
REFERENCES
......................................................163
7
HAMILTONIAN
MONODROMY
AS
LATTICE
DEFECT
B.
ZHILINSKII
.....................................................
165
7.1
INTRODUCTION
.................................................165
7.2
INTEGRABLE
CLASSICAL
SINGULAR
FIBRATIONS
AND
MONODROMY
..........165
7.3
QUANTUMMONODROMY
........................................167
7.4
ELEMENTARY
DEFECTS
OF
LATTICES
.................................168
7.4.1VACATIONS
AND
LINEAR
DISLOCATIONS
.........................169
7.4.2ANGULAR
DISLOCATIONS
AS
ELEMENTARY
MONODROMY
DEFECT
......170
7.4.3ABOUT
THE
SIGN
OF
THE
ELEMENTARY
MONODROMY
DEFECT
........171
7.4.4RATIONAL
CUTS
AND
RATIONAL
LINE
DEFECTS
...................172
7.5
DEFECTS
WITH
ARBITRARY
MONODROMY.............................175
7.5.1TOPOLOGICAL
DESCRIPTION
OF
UNIMODULAR
MATRICES
.............175
7.5.2CLASSES
OF
CONJUGATED
ELEMENTS
AND
NORMAL
FORM
OF
SL
(2
,Z
)MATRICES
.......................................177
7.5.3SEVERAL
ELEMENTARY
MONODROMY
DEFECTS
....................177
7.5.4SEVERAL
RATIONAL
LINE
DEFECTS
.............................181
7.6
IS
THERE
MUTUAL
INTEREST
IN
DEFECT
-
MONODROMY
CORRESPONDENCE?
.183
REFERENCES
......................................................185
XC
O
N
T
E
N
T
S
8
TWO-QUBITANDTHREE-QUBIT
GEOMETRYANDHOPFFIBRATIONS
R.
MOSSERI
.....................................................
187
8.1
INTRODUCTION
.................................................187
8.2
FROM
THE
S
3
HYPERSPHERE
TO
THE
BLOCH
SPHERE
REPRESENTATION
.....188
8.3
TWO
QUBITS,
ENTANGLEMENT,
AND
THE
S
7
HOPF
FIBRATION............190
8.3.1THE
TWO-QUBIT
HILBERT
SPACE
.............................190
8.3.2THE
S
7
HOPF
FIBRATION
...................................190
8.3.3GENERALIZED
BLOCH
SPHERE
FOR
THE
TWO-QUBIT
CASE
...........192
8.4
THREE
QUBITS
AND
THE
S
15
HOPF
FIBRATION
.......................197
8.4.1THREE
QUBITS............................................197
8.4.2THE
S
15
HOPF
FIBRATION
..................................197
8.4.3DISCUSSION
..............................................198
8.5
CONCLUSIONS..................................................200
REFERENCES
......................................................203
9
DEFECTS,
SURFACE
ANCHORING,
AND
THREE-DIMENSIONAL
DIRECTOR
FIELDS
IN
THE
LAMELLAR
STRUCTURE
OF
CHOLESTERIC
LIQUID
CRYSTALS
AS
STUDIED
BY
FLUORESCENCE
CONFOCAL
POLARIZING
MICROSCOPY
I.I.
SMALYUKH
AND
O.D.
LAVRENTOVICH
...............................
205
9.1
INTRODUCTION
.................................................205
9.2
EXPERIMENTAL
METHODS
AND
MATERIALS
...........................207
9.2.1MATERIALS
AND
CELL
PREPARATION
............................207
9.2.2FLUORESCENCE
CONFOCAL
POLARIZING
MICROSCOPY
................208
9.3
DIRECTORS
AND
DEFECTS
IN
CHOLESTERIC
LIQUID
CRYSTALS
..............209
9.4
ELASTIC
AND
SURFACE
PROPERTIES
OF
CHOLESTERICS
....................210
9.4.1ELASTICITY
OF
CHOLESTERIC
LIQUID
CRYSTALS
....................211
9.4.2SURFACE
ANCHORING
ENERGY
................................213
9.5
DISLOCATION-INTERFACE
INTERACTION
AND
THREE-DIMENSIONAL
DIRECTOR
STRUCTURES
IN
THE
WEAKLY
ANCHORED
CHOLESTERICS
.........216
9.5.1ANCHORING-MEDIATED
DISLOCATION-INTERFACE
INTERACTION
........216
9.5.2LAYERS
PROFILES
OF
ISOLATED
EDGE
DISLOCATIONS
................220
9.6
THE
EQUILIBRIUM
DEFECTS
AND
STRUCTURES
IN
STRONGLY
ANCHORED
CHOLESTERICWEDGES...........................................222
9.6.1EXPERIMENTAL
OBSERVATIONS................................223
9.6.2FAR-FIELD
ENERGY
OF
AN
ISOLATED
DISLOCATION
.................226
9.6.3DISLOCATION
CORE
ENERGY..................................227
9.6.4EFFECT
OF
CONFINEMENT
ON
THE
DISLOCATION
ENERGY.............228
9.6.5EQUILIBRIUM
LATTICE
OF
DISLOCATION
IN
A
CHOLESTERIC
WEDGE.....228
9.7
METASTABLE
STRUCTURES,
OILY
STREAKS,
TURNS
AND
NODES
OF
DEFECTS
...230
9.7.1METASTABLE
STRUCTURES
AND
OILY
STREAKS.....................230
9.7.2DISLOCATION
TURNS........................................234
9.7.3NODES
OF
LINE
DEFECTS
....................................235
9.8
DYNAMICS
OF
DEFECTS,
GLIDE
AND
CLIMB
OF
DISLOCATIONS,
AND
THEIR
KINKS.......................................................237
CONTENTS
XI
9.8.1PEACH
AND
KOEHLER
FORCE
.................................238
9.8.2CLIMB
..................................................238
9.8.3GLIDE...................................................239
9.8.4EXPERIMENTAL
OBSERVATIONS
...............................240
9.8.5PEIERLS-NABARRO
FRICTION
..................................244
9.8.6KINK
STRUCTURE
VERSUS
PEIERLS-NABARRO
ENERGY
BARRIER
.......246
9.9
CONCLUSIONS..................................................247
REFERENCES
......................................................249
INDEX
..........................................................
251
|
| adam_txt |
CONTENTS
INTRODUCTION
M.
MONASTYRSKY
.
1
1
TOPOLOGY
IN
THE
ELECTRON
THEORY
OF
METALS
A.M.
KOSEVICH
.
3
1.1
INTRODUCTION
.
3
1.2
DYNAMICS
OF
CONDUCTIVITY
ELECTRONS
AND
THE
FERMI
SURFACE
.
4
1.3
GEOMETRY
OF
THE
FERMI
SURFACE
IN
CRYSTAL
.
8
1.4
QUANTUM
MAGNETIC
OSCILLATIONS
AND
THE
SHAPE
OF
THE
FERMI
SURFACE
11
1.5
MAGNETICBREAKDOWN
.
16
1.6
BAND
ELECTRONS
IN
THE
ELECTRIC
FIELD
AND
BLOCH
OSCILLATIONS
.
17
1.7
TOPOLOGY
OF
THE
FERMI
SURFACES
AND
LOW-TEMPERATURE
MAGNETORESISTIVITY
OF
METALS
.
19
1.8
BERRY'S
PHASE
AND
THE
TOPOLOGY
OF
THE
ELECTRON
TRAJECTORIES
IN
THE
MAGNETICFIELD.
23
REFERENCES
.
28
2
TOPOLOGY,
QUASIPERIODIC
FUNCTIONS,
AND
THE
TRANSPORT
PHENOMENA
A.YA.
MALTSEV
AND
S.P.
NOVIKOV
.
31
2.1
INTRODUCTION
.
31
2.1.1GALVANOMAGNETIC
PHENOMENA
IN
NORMAL
METALS:
CLASSICAL
RESULTS,
GSMF
LIMIT
.
31
2.1.2MODERN
IDEAS:
THE
GSMF
LIMIT,
TOPOLOGY,
AND
DYNAMICAL
SYSTEMS
.
36
2.1.3TRANSPORT
IN
2D
ELECTRON
GAS
AND
TOPOLOGY
OF
QUASIPERIODIC
FUNCTIONS.
39
2.2
THECLASSIFICATIONOFFERMISURFACESANDTHE"TOPOLOGICALQUANTUM
NUMBERS".
41
VIII
CONTENTS
2.3
QUASIPERIODICMODULATIONSOF2DELECTRONGASANDTHEGENERALIZED
NOVIKOVPROBLEM.
49
REFERENCES
.
58
3
THE
ROLE
OF
TOPOLOGY
IN
GROWTH
AND
AGGLOMERATION
R.
KERNER
.
61
3.1
INTRODUCTION
.
61
3.2
TOPOLOGY
AND
GEOMETRY
OF
POLYGON
TILINGS
AND
NETWORKS
.
62
3.3
DYNAMICAL
MODEL
OF
POLYGON
AGGLOMERATION
IN
TWO
DIMENSIONS
.
69
3.4
APPLICATION:
HOW
THE
FULLERENE
MOLECULES
ARE
FORMED.
74
3.5
ONION
FULLERENES
AND
CARBON
TUBES
.
79
3.6
RIGIDITY
AND
LOCAL
STRUCTURE
IN
COVALENT
GLASSES
.
85
REFERENCES
.
90
4
TOPOLOGICAL
DEFECTS
IN
CARBON
NANOCRYSTALS
V.A.
OSIPOV
.
93
4.1
INTRODUCTION
.
93
4.2
GEOMETRY
AND
TOPOLOGY
OF
CARBON
NANOPARTICLES.
94
4.3
ELECTRONICPROPERTIES
.
98
4.3.1THEORY:
BASIC
ASSUMPTIONS
.
99
4.4
SPHERICAL
MOLECULES.102
4.4.1THE
MODEL.102
4.4.2EXTENDED
ELECTRON
STATES
.104
4.4.3NUMERICAL
RESULTS
.105
4.4.4ZERO-ENERGY
MODES
.106
4.5
NANOCONES.107
4.5.1THE
MODEL.107
4.5.2ELECTRON
STATES
.108
4.5.3NUMERICAL
RESULTS
.110
4.6
HYPERBOLOID
GEOMETRY.110
4.6.1THE
MODEL.110
4.6.2ELECTRON
STATES
.111
4.6.3NUMERICAL
RESULTS
.113
4.7
CONCLUSIONS.114
REFERENCES
.115
5
PHYSICS
FROM
TOPOLOGY
AND
STRUCTURES
J.
YI
.
117
5.1
INTRODUCTION
.117
5.2
QUANTUMHALLEFFECT.118
5.3
SHAPIRO
STEPS
IN
JOSEPHSON
JUNCTIONS
.122
5.4
CHARGEDENSITYWAVES
.126
5.5
QUANTUMPHASES.129
5.6
CARBONNANOTUBES
.132
CONTENTS
IX
5.7
CONCLUSIONS.136
REFERENCES
.136
6
PHASON
DYNAMICS
IN
APERIODIC
CRYSTALS
T.
JANNSEN
.
139
6.1
INTRODUCTION
.139
6.1.1QUASIPERIODIC
CRYSTALS
.139
6.1.2EXAMPLES
OF
QUASIPERIODIC
CRYSTALS
.140
6.1.3SYMMETRY
.141
6.2
EMBEDDING
IN
SUPERSPACE
.143
6.3
SIMPLE
MODELS
FOR
INCOMMENSURATE
STRUCTURES
.145
6.3.1DISPLACIVELY
MODULATED
PHASES
.145
6.3.2THE
DOUBLE-CHAIN
MODEL
FOR
INCOMMENSURATE
COMPOSITES
.147
6.3.3THE
GROUND
STATE
OF
THE
DCM
.147
6.4
PHONONSANDPHASONS.148
6.4.1PHONONS
IN
APERIODIC
CRYSTALS
.148
6.4.2PHASON
EXCITATIONS
.151
6.4.3THE
PHASON
CONTENT
OF
PHONONS.153
6.5
NONLINEAR
PHASON
DYNAMICS
.154
6.5.1MODULATED
PHASES
.154
6.5.2INCOMMENSURATE
COMPOSITES
.155
6.6
SLIDING
ON
A
QUASIPERIODIC
SUBSTRATE.160
6.6.1A
MODEL.160
6.6.2NONLINEAR
DYNAMICS
AND
FRICTION
.162
6.7
CONCLUSIONS.162
REFERENCES
.163
7
HAMILTONIAN
MONODROMY
AS
LATTICE
DEFECT
B.
ZHILINSKII
.
165
7.1
INTRODUCTION
.165
7.2
INTEGRABLE
CLASSICAL
SINGULAR
FIBRATIONS
AND
MONODROMY
.165
7.3
QUANTUMMONODROMY
.167
7.4
ELEMENTARY
DEFECTS
OF
LATTICES
.168
7.4.1VACATIONS
AND
LINEAR
DISLOCATIONS
.169
7.4.2ANGULAR
DISLOCATIONS
AS
ELEMENTARY
MONODROMY
DEFECT
.170
7.4.3ABOUT
THE
SIGN
OF
THE
ELEMENTARY
MONODROMY
DEFECT
.171
7.4.4RATIONAL
CUTS
AND
RATIONAL
LINE
DEFECTS
.172
7.5
DEFECTS
WITH
ARBITRARY
MONODROMY.175
7.5.1TOPOLOGICAL
DESCRIPTION
OF
UNIMODULAR
MATRICES
.175
7.5.2CLASSES
OF
CONJUGATED
ELEMENTS
AND
"NORMAL
FORM"
OF
SL
(2
,Z
)MATRICES
.177
7.5.3SEVERAL
ELEMENTARY
MONODROMY
DEFECTS
.177
7.5.4SEVERAL
RATIONAL
LINE
DEFECTS
.181
7.6
IS
THERE
MUTUAL
INTEREST
IN
DEFECT
-
MONODROMY
CORRESPONDENCE?
.183
REFERENCES
.185
XC
O
N
T
E
N
T
S
8
TWO-QUBITANDTHREE-QUBIT
GEOMETRYANDHOPFFIBRATIONS
R.
MOSSERI
.
187
8.1
INTRODUCTION
.187
8.2
FROM
THE
S
3
HYPERSPHERE
TO
THE
BLOCH
SPHERE
REPRESENTATION
.188
8.3
TWO
QUBITS,
ENTANGLEMENT,
AND
THE
S
7
HOPF
FIBRATION.190
8.3.1THE
TWO-QUBIT
HILBERT
SPACE
.190
8.3.2THE
S
7
HOPF
FIBRATION
.190
8.3.3GENERALIZED
BLOCH
SPHERE
FOR
THE
TWO-QUBIT
CASE
.192
8.4
THREE
QUBITS
AND
THE
S
15
HOPF
FIBRATION
.197
8.4.1THREE
QUBITS.197
8.4.2THE
S
15
HOPF
FIBRATION
.197
8.4.3DISCUSSION
.198
8.5
CONCLUSIONS.200
REFERENCES
.203
9
DEFECTS,
SURFACE
ANCHORING,
AND
THREE-DIMENSIONAL
DIRECTOR
FIELDS
IN
THE
LAMELLAR
STRUCTURE
OF
CHOLESTERIC
LIQUID
CRYSTALS
AS
STUDIED
BY
FLUORESCENCE
CONFOCAL
POLARIZING
MICROSCOPY
I.I.
SMALYUKH
AND
O.D.
LAVRENTOVICH
.
205
9.1
INTRODUCTION
.205
9.2
EXPERIMENTAL
METHODS
AND
MATERIALS
.207
9.2.1MATERIALS
AND
CELL
PREPARATION
.207
9.2.2FLUORESCENCE
CONFOCAL
POLARIZING
MICROSCOPY
.208
9.3
DIRECTORS
AND
DEFECTS
IN
CHOLESTERIC
LIQUID
CRYSTALS
.209
9.4
ELASTIC
AND
SURFACE
PROPERTIES
OF
CHOLESTERICS
.210
9.4.1ELASTICITY
OF
CHOLESTERIC
LIQUID
CRYSTALS
.211
9.4.2SURFACE
ANCHORING
ENERGY
.213
9.5
DISLOCATION-INTERFACE
INTERACTION
AND
THREE-DIMENSIONAL
DIRECTOR
STRUCTURES
IN
THE
WEAKLY
ANCHORED
CHOLESTERICS
.216
9.5.1ANCHORING-MEDIATED
DISLOCATION-INTERFACE
INTERACTION
.216
9.5.2LAYERS
PROFILES
OF
ISOLATED
EDGE
DISLOCATIONS
.220
9.6
THE
EQUILIBRIUM
DEFECTS
AND
STRUCTURES
IN
STRONGLY
ANCHORED
CHOLESTERICWEDGES.222
9.6.1EXPERIMENTAL
OBSERVATIONS.223
9.6.2FAR-FIELD
ENERGY
OF
AN
ISOLATED
DISLOCATION
.226
9.6.3DISLOCATION
CORE
ENERGY.227
9.6.4EFFECT
OF
CONFINEMENT
ON
THE
DISLOCATION
ENERGY.228
9.6.5EQUILIBRIUM
LATTICE
OF
DISLOCATION
IN
A
CHOLESTERIC
WEDGE.228
9.7
METASTABLE
STRUCTURES,
OILY
STREAKS,
TURNS
AND
NODES
OF
DEFECTS
.230
9.7.1METASTABLE
STRUCTURES
AND
OILY
STREAKS.230
9.7.2DISLOCATION
TURNS.234
9.7.3NODES
OF
LINE
DEFECTS
.235
9.8
DYNAMICS
OF
DEFECTS,
GLIDE
AND
CLIMB
OF
DISLOCATIONS,
AND
THEIR
KINKS.237
CONTENTS
XI
9.8.1PEACH
AND
KOEHLER
FORCE
.238
9.8.2CLIMB
.238
9.8.3GLIDE.239
9.8.4EXPERIMENTAL
OBSERVATIONS
.240
9.8.5PEIERLS-NABARRO
FRICTION
.244
9.8.6KINK
STRUCTURE
VERSUS
PEIERLS-NABARRO
ENERGY
BARRIER
.246
9.9
CONCLUSIONS.247
REFERENCES
.249
INDEX
.
251 |
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| any_adam_object_boolean | 1 |
| author2 | Monastyrskij, Michail I. 1945- |
| author2_role | edt |
| author2_variant | m i m mi mim |
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| author_facet | Monastyrskij, Michail I. 1945- |
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| classification_rvk | UP 1100 UP 1300 |
| classification_tum | PHY 014f PHY 602f |
| ctrlnum | (OCoLC)181440634 (DE-599)BVBBV021329345 |
| discipline | Physik |
| discipline_str_mv | Physik |
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| id | DE-604.BV021329345 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:01:12Z |
| indexdate | 2024-07-09T20:35:48Z |
| institution | BVB |
| isbn | 9783540234067 3540234063 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014649659 |
| oclc_num | 181440634 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-91G DE-BY-TUM DE-83 DE-11 |
| owner_facet | DE-29T DE-703 DE-91G DE-BY-TUM DE-83 DE-11 |
| physical | XIV, 254 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in solid-state sciences |
| series2 | Springer series in solid-state sciences |
| spelling | Topology in condensed matter M. I. Monastyrsky (ed.) Berlin [u.a.] Springer 2006 XIV, 254 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 150 Literaturangaben This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form. TOC:Introduction.- Phason Dynamics in Aperiodic Crystals.- Defects, Surface Anchoring and Three-Dimensional Director Fields in the Lamellar Structure of Cholesteric Liquid Crystals.- Topology, Quasiperiodic Functions and the Transport Phenomena.- Topology in the Electron Theory of Metals.- Topological Defects in Carbon Nanocrystals.- Physics from Topology and Structures.- Two and Three Qubits Geometry and Hopf Fibrations.- Hamiltonian Monodromy as Lattice Defect.- Topology of Glasses Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Topologische Methode (DE-588)4312758-7 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 s Mathematische Physik (DE-588)4037952-8 s Topologische Methode (DE-588)4312758-7 s DE-604 Monastyrskij, Michail I. 1945- (DE-588)121283623 edt Springer series in solid-state sciences 150 (DE-604)BV000016582 150 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014649659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topology in condensed matter Springer series in solid-state sciences Mathematische Physik (DE-588)4037952-8 gnd Topologische Methode (DE-588)4312758-7 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4312758-7 (DE-588)4132810-3 |
| title | Topology in condensed matter |
| title_auth | Topology in condensed matter |
| title_exact_search | Topology in condensed matter |
| title_exact_search_txtP | Topology in condensed matter |
| title_full | Topology in condensed matter M. I. Monastyrsky (ed.) |
| title_fullStr | Topology in condensed matter M. I. Monastyrsky (ed.) |
| title_full_unstemmed | Topology in condensed matter M. I. Monastyrsky (ed.) |
| title_short | Topology in condensed matter |
| title_sort | topology in condensed matter |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Topologische Methode (DE-588)4312758-7 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| topic_facet | Mathematische Physik Topologische Methode Kondensierte Materie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014649659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016582 |
| work_keys_str_mv | AT monastyrskijmichaili topologyincondensedmatter |