Quantum chaos and quantum dots:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2006
|
| Edition: | reprint. |
| Series: | Mesoscopic physics and nanotechnology
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 199 S. Ill., graph. Darst. |
| ISBN: | 0198525893 9780198525899 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quantum chaos and quantum dots |c Katsuhiro Nakamura ; Takahisa Harayama |
| 250 | |a reprint. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2006 | |
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Record in the Search Index
| _version_ | 1804138079105056768 |
|---|---|
| adam_text | CONTENTS
1 Quantum Chaos
and Billiards
1
1.1
Birth of the Physics of Billiards
1
1.2
What is Quantum Chaos?
3
1.3
Resistance of Quantum Dots
4
1.4
Dynamics in Billiards and Semiclassical Theory
7
2
Quantum Transport and Chaos in Billiards
11
2.1
Quantum Theory of Conductance
11
2.2
Semiclassical Approximation and Stationary-Phase Method
12
2.3
Semiclassical Green Function and Transmission Amplitude
13
2.4
Autocorrelation Function
15
2.5
Conductance and Area Distribution
15
3
Motion of a Billiard Ball
18
3.1
Expanding
Wavefront
and Lyapunov Exponent
18
3.2
Birkhoff Coordinates and the
Repeller
27
3.3
Kolmogorov-Sinai Entropy and Escape Rate
31
3.4
Area Distribution
36
4
Semiclassical Theory of Conductance Fluctuations
41
4.1
Quantum Billiards with Lead Wires
41
4.2
Semiclassical Green Function
43
4.3
Transmission Coefficients
52
4.4
Conductance Fluctuations
55
5
Semiclassical Quantization and Thermodynamics of Meso-
scopic Systems
60
5.1
Semiclassical Quantization of Chaos and Regular Orbits
60
5.1.1
Berry-Tabor s Trace Formula
64
5.1.2
Gutzwiller s Trace Formula
66
5.2
Thermodynamics of Mesoscopic Systems
72
5.2.1
Grand Canonical Ensemble
72
5.2.2
Canonical Ensemble
76
6
Orbital Diamagnetism and Persistent Current
79
6.1
Historical Background
79
6.2
Orbital Diamagnetism in the Light of Nonlinear Dynamics
81
6.3
Semiclassical Orbital Diamagnetism in 3-d Billiards
86
6.3.1
Integrable
(Spherical Shell) Billiards
89
6.3.2
Fully Chaotic Billiards
93
6.4
Semiclassical Persistent Current in 3-d Shell Billiards
94
7
Quantum Interference in Single Open Billiards
98
χ
CONTENTS
7.1
Chaos and Quantum Transport
98
7.2
Ballistic Weak Localization (WL)
101
7.3
Criticism against the Semiclassical Theory of Ballistic WL
105
7.4
Ballistic
AAS
Oscillation
108
7.5
Effects of Small-Angle Induced Diffraction 111
7.5.1
Partial Time-Reversal Symmetry and Ballistic Weak-
Localization Correction
112
7.5.2
Semiclassical Derivation of Universal Conductance
Fluctuations
115
7.6
Self-Similar Magneto-Conductance Fluctuations
120
7.6.1
Harmonic Saddles as the Origin of Self-Similarity
122
7.6.2
Scaling Properties
127
8
Linear Response Theory in the Semiclassical Regime
130
8.1
Realization of Sinai Billiards
130
8.2
Semiclassical Shubnikov-de Haas Oscillation
132
8.3
Semiclassical
Kubo
Formula in
Antidot Superlattices
138
8.3.1
Drude
Conductivity
139
8.3.2
Quantum Correction
140
8.4
Effect of Finite Temperature and Spin
142
8.5
Interpretation of Experiments
143
9
Orbit Bifurcations, Arnold Diffusion, and Coulomb Block¬
ade
145
9.1
Orbit Bifurcations in Triangular
Antidot
Lattices
145
9.1.1
Semiclassical Conductivity and Orbit Bifurcations
149
9.1.2
Quantum Correction without Orbit Bifurcations
151
9.1.3
Orbit Bifurcations and Anomalous Resistivity Fluc¬
tuations
154
9.2
Arnold Diffusion and Negative Magneto-Resistance
157
9.2.1
Semiclassical Conductance for Open Three-Dimensional
Billiards
157
9.2.2
Completely or Partially Broken-Ergodic 3-d Billiards
159
9.2.3
Effects of Symmetry-Breaking Weak Magnetic Field
161
9.3
Semiclassical Theory of Coulomb Blockade
166
9.3.1
Peak Height and Wavefunction
168
9.3.2
Peak Height Distribution
169
10
Nonadiabatic Transitions, Energy Diffusion and Gener¬
alized Friction
174
10.1
What is Energy Diffusion?
174
10.2
What is Level Statistics?
175
10.3
Energy Diffusion: Landau-Zener regime
178
10.4
Energy Diffusion: Linear-Response Regime
181
10.5
Frictional Force due to Nonadiabatic Transition
183
10.6
Future Prospects
186
CONTENTS xi
References
189
Index 195
|
| adam_txt |
CONTENTS
1 Quantum Chaos
and Billiards
1
1.1
Birth of the Physics of Billiards
1
1.2
What is Quantum Chaos?
3
1.3
Resistance of Quantum Dots
4
1.4
Dynamics in Billiards and Semiclassical Theory
7
2
Quantum Transport and Chaos in Billiards
11
2.1
Quantum Theory of Conductance
11
2.2
Semiclassical Approximation and Stationary-Phase Method
12
2.3
Semiclassical Green Function and Transmission Amplitude
13
2.4
Autocorrelation Function
15
2.5
Conductance and Area Distribution
15
3
Motion of a Billiard Ball
18
3.1
Expanding
Wavefront
and Lyapunov Exponent
18
3.2
Birkhoff Coordinates and the
Repeller
27
3.3
Kolmogorov-Sinai Entropy and Escape Rate
31
3.4
Area Distribution
36
4
Semiclassical Theory of Conductance Fluctuations
41
4.1
Quantum Billiards with Lead Wires
41
4.2
Semiclassical Green Function
43
4.3
Transmission Coefficients
52
4.4
Conductance Fluctuations
55
5
Semiclassical Quantization and Thermodynamics of Meso-
scopic Systems
60
5.1
Semiclassical Quantization of Chaos and Regular Orbits
60
5.1.1
Berry-Tabor's Trace Formula
64
5.1.2
Gutzwiller's Trace Formula
66
5.2
Thermodynamics of Mesoscopic Systems
72
5.2.1
Grand Canonical Ensemble
72
5.2.2
Canonical Ensemble
76
6
Orbital Diamagnetism and Persistent Current
79
6.1
Historical Background
79
6.2
Orbital Diamagnetism in the Light of Nonlinear Dynamics
81
6.3
Semiclassical Orbital Diamagnetism in 3-d Billiards
86
6.3.1
Integrable
(Spherical Shell) Billiards
89
6.3.2
Fully Chaotic Billiards
93
6.4
Semiclassical Persistent Current in 3-d Shell Billiards
94
7
Quantum Interference in Single Open Billiards
98
χ
CONTENTS
7.1
Chaos and Quantum Transport
98
7.2
Ballistic Weak Localization (WL)
101
7.3
Criticism against the Semiclassical Theory of Ballistic WL
105
7.4
Ballistic
AAS
Oscillation
108
7.5
Effects of Small-Angle Induced Diffraction 111
7.5.1
Partial Time-Reversal Symmetry and Ballistic Weak-
Localization Correction
112
7.5.2
Semiclassical Derivation of Universal Conductance
Fluctuations
115
7.6
Self-Similar Magneto-Conductance Fluctuations
120
7.6.1
Harmonic Saddles as the Origin of Self-Similarity
122
7.6.2
Scaling Properties
127
8
Linear Response Theory in the Semiclassical Regime
130
8.1
Realization of Sinai Billiards
130
8.2
Semiclassical Shubnikov-de Haas Oscillation
132
8.3
Semiclassical
Kubo
Formula in
Antidot Superlattices
138
8.3.1
Drude
Conductivity
139
8.3.2
Quantum Correction
140
8.4
Effect of Finite Temperature and Spin
142
8.5
Interpretation of Experiments
143
9
Orbit Bifurcations, Arnold Diffusion, and Coulomb Block¬
ade
145
9.1
Orbit Bifurcations in Triangular
Antidot
Lattices
145
9.1.1
Semiclassical Conductivity and Orbit Bifurcations
149
9.1.2
Quantum Correction without Orbit Bifurcations
151
9.1.3
Orbit Bifurcations and Anomalous Resistivity Fluc¬
tuations
154
9.2
Arnold Diffusion and Negative Magneto-Resistance
157
9.2.1
Semiclassical Conductance for Open Three-Dimensional
Billiards
157
9.2.2
Completely or Partially Broken-Ergodic 3-d Billiards
159
9.2.3
Effects of Symmetry-Breaking Weak Magnetic Field
161
9.3
Semiclassical Theory of Coulomb Blockade
166
9.3.1
Peak Height and Wavefunction
168
9.3.2
Peak Height Distribution
169
10
Nonadiabatic Transitions, Energy Diffusion and Gener¬
alized Friction
174
10.1
What is Energy Diffusion?
174
10.2
What is Level Statistics?
175
10.3
Energy Diffusion: Landau-Zener regime
178
10.4
Energy Diffusion: Linear-Response Regime
181
10.5
Frictional Force due to Nonadiabatic Transition
183
10.6
Future Prospects
186
CONTENTS xi
References
189
Index 195 |
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| id | DE-604.BV035107951 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:16:30Z |
| indexdate | 2024-07-09T21:22:29Z |
| institution | BVB |
| isbn | 0198525893 9780198525899 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016775832 |
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| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM |
| physical | XI, 199 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Mesoscopic physics and nanotechnology |
| series2 | Mesoscopic physics and nanotechnology |
| spelling | Nakamura, Katsuhiro Verfasser aut Quantum chaos and quantum dots Katsuhiro Nakamura ; Takahisa Harayama reprint. Oxford [u.a.] Oxford Univ. Press 2006 XI, 199 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mesoscopic physics and nanotechnology 3 Quantenchaos Quantenpunkt (DE-588)4263396-5 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf Quantenchaos (DE-588)4130849-9 s Quantenpunkt (DE-588)4263396-5 s DE-604 Harayama, Takahisa Verfasser aut Mesoscopic physics and nanotechnology 3 (DE-604)BV011705218 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016775832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nakamura, Katsuhiro Harayama, Takahisa Quantum chaos and quantum dots Mesoscopic physics and nanotechnology Quantenchaos Quantenpunkt (DE-588)4263396-5 gnd Quantenchaos (DE-588)4130849-9 gnd |
| subject_GND | (DE-588)4263396-5 (DE-588)4130849-9 |
| title | Quantum chaos and quantum dots |
| title_auth | Quantum chaos and quantum dots |
| title_exact_search | Quantum chaos and quantum dots |
| title_exact_search_txtP | Quantum chaos and quantum dots |
| title_full | Quantum chaos and quantum dots Katsuhiro Nakamura ; Takahisa Harayama |
| title_fullStr | Quantum chaos and quantum dots Katsuhiro Nakamura ; Takahisa Harayama |
| title_full_unstemmed | Quantum chaos and quantum dots Katsuhiro Nakamura ; Takahisa Harayama |
| title_short | Quantum chaos and quantum dots |
| title_sort | quantum chaos and quantum dots |
| topic | Quantenchaos Quantenpunkt (DE-588)4263396-5 gnd Quantenchaos (DE-588)4130849-9 gnd |
| topic_facet | Quantenchaos Quantenpunkt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016775832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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