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Nakamura K., Harayama T. — Quantum chaos and quantum dots
Nakamura K., Harayama T. — Quantum chaos and quantum dots

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Название: Quantum chaos and quantum dots

Авторы: Nakamura K., Harayama T.

Аннотация:

Dynamics of billiard balls and their role in physics have received wide attention. Billiards can nowadays be created as quantum dots in the microscopic world enabling one to envisage the so-called quantum chaos, (i.e.: quantum manifestation of chaos of billiard balls). In fact, owing to recent progress in advanced technology, nanoscale quantum dots, such as chaotic stadium and antidot lattices analogous to the Sinai Billiard, can be fabricated at the interface of semiconductor heterojunctions. This book begins ite exploration of the effect of chaotic electron dynamics on ballistic quantum transport in quantum dots with a puzzling experiment on resistance fluctuations for stadium and circle dots. Throughout the text, major attention is paid to the semiclassical theory which makes it possible to interpret quantum phenomena in the language of the classical world. Chapters one to four are concerned with the elementary statistical methods (curvature, Lyapunov exponent, Kolmogorov-Sinai entropy and escape rate), which are needed for a semiclassical description of transport in quantum dots. Chapters five to ten discuss the topical subjects in the field, including the ballistic weak localization, Altshuler-Aronov-Spivak oscillation, partial time-reversal symmetry, persistent current, Arnold diffusion and Coulomb blockade.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 208

Добавлена в каталог: 23.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$S$ matrix      43 158
$SO$(2)-symmetric billiards      159
$SO$(3)-symmetry      70 89
$U$(1) symmetry      70
AAS oscillation      108
AB oscillation      108
Accumulated density of states      72
Action-angle variables      66
Addition energy      166
Adiabatic invariants      64
Adiabatic spectrum      174
Advanced Green function      61 134 136
Aharonov - Bohm (AB) billiards      108
Aharonov - Bohm (AB) effect      81 94 108
algorithmic complexity      31
Altshuler - Aronov - Spivak (AAS) oscillation      108
Anderson localization      101
Antidot lattice      145
Antidot superlattices      138
Antidots      130
Area distribution      17 37 58
Area-preserving      31
Arnold diffusion (AD)      157 162
Arnold web (AW)      162
Aspect ratio      120
Autocorrelation function      5 15 100
Avoided crossings among energy levels      84
Back-scattering orbits      102
Ballistic motion      3 7 98
Ballistic weak localization      101 105
Berry - Tabor trace formula      64
Billiard (circle)      101
Billiard (stadium)      101
Billiard ball      7
Birkhoff coordinates      81 163
Birkhoff pair of coordinates      28
Born factor      139
Broken-ergodic 3-d billiards      159
Bulk quantum transport      132
canonical ensemble      72
Change of the wavefront caused by the collision      22
Chaos      7
Chaotic sea      66
Charging energy      166
chemical potential      73
circle      6
Classical reflection probability      102 117
Classical transmission probabilities      117
Classical-mechanical transmission      15
Commensurate cyclotron orbits      149
Commensurate orbits      131
Complete Larmor orbit      136
Completely integrable      64 86
Composite fermions      144
Conductance      43 122
Conductance distribution      170
Conductance fluctuations      55 115
Conjugate points      63
Continuous symmetry      70
Convex (or swollen)      130
Convolution      16 59
Cooperon      116
Correspondence principle      10
Coulomb blockade      166
Coulomb oscillation      166
Criticism against semiclassical theory of ballistic WL      105
Current conservation law      106
Curvature for the wavefront      21
Curvature of individual levels      84
Curvature of the billiard table wall      23
Cusp-like      101
Cutoff time      75
Cyclotron frequency      135
cyclotron motion      79
Damping factor      75 142
de Broglie wavelength      10
De Haas-van Alphen oscillation      81
Deformation of periodic orbits      149
Density of states      61 72
Density operator      184
Diamagnetic moment      79
diamagnetic susceptibility      80
Diffraction-catastrophe integral      151
Diffusion constant      180 182
Diffuson      115
Discrete map      81
Distribution for avoided crossing      180
Double square billiard      110
Double tunneling      168
Drude conductivity      100 139
Dwelling time distribution      110
Edge current      80
Effective transition rate      182
Einstein - Brillouin - Keller (EBK) quantization rule      66
Elastic scattering time      134
Electrical conductivity      185
Ellipsoid      163
Elliptic billiard system      81
Energy diffusion      174
Energy gap      178
Energy level crossings      176
Energy shell      185
Ensemble-averaged susceptibility      93
Ensemble-averaged value      88
Ensemble-mean values      78
Ergodicity hypothesis      1
Escape rate      34 116
Euler angle      94
Exact self-similarity      127
Expanding wavefront      18
Exponential distribution      59
Extended semiclassical theory      112
Fermi - Dirac distribution function      73
Fermi Golden Rule      168
Feynman path-integral method      61
Finite-temperature effect      76
Fisher - Lee formula      44
Flower-like billiard      2
Flux quanta      91 102 185
Fractal structure      122
Free Green function      44 52
Frictional force      175 183
Fully chaotic      86
Fully chaotic systems without bifurcations      66
Functional integral      61
Gate voltage      166
Gauge potential      109
grand canonical ensemble      72
Great circular plane      89 94
Green function      12 43 61
Gutzwilier trace formula      66 69
Hamilton - Jacobi equation      67
Hankel function      44
Hannay and Ozorio de Almeida (H - OdA) sum rule      153
Harmonic saddle      125
Heller wavefunction scars      173
Helmholtz free energy      76
Henon - Heiles potential      126
Heterojunction      6 130
Hierarchical island structure      122
Improved trace formula      71
Incomplete orbit      136
Individual value      78
Invariant tori      82
Irreducible closed paths      64
Irreducible part      136
Islands structure      122
Isochronous bifurcations      127
Isochronous pitchfork bifurcations      123
Joint probability density      177
Kolmogorov - Arnold - Moser (KAM) tori      82 110 162
Kolmogorov - Sinai (KS) entropy      31 33 70
Kubo - Greenwood method      181
Kubo formula      100 111 134
Landau - Zener regime      178
Landau levels      80
Landau susceptibility      84
Landauer formula      11 43 102 106 115
Larmor orbit      79 135
Law of reflection      14
Lead orientation      163
Lead wires      11 101
Legendre transformation      76
Level gradient      178
Librating periodic orbit      127
Linear response      178
Linearized Poincare map      68
Liouville’s theorem      86
Longitudinal conductivity      134
Loop current      79
Lorentz gas      130
Lorentzian      59 101
Lyapunov exponent      26 36 100
Macroscopic variables      175
Magnetic flux      94
Magnetic-field dependence of resistance      6
Magneto-resistance      120
Maslov index      68 71 158
Master equation      180
Maxwell - Boltzmann (MB) distribution      1
Mean part      65 72
Mixed billiards      111
Mixed system      122
Monodromy matrix      68 164
Multiple scattering expansion      44
Multiply connected structure      94
Negative magneto-resistance      101 157
Non - Gaussian distribution      167
Nonadiabatic transitions      174
Nonlinear Schrodinger equation      187
Nonlocal potential      150
Ohm law      185
One dimensional metallic ring      111
Open 3-d billiards      157
Orbit bifurcations      70 150
Orbital diamagnetism      79
Oscillating part      65 72 88
Pair of anomalous orbits      113
Pair-propagator      113 115
Partially-time reversal symmetric      113
Particle-number conservation law      116
Partition function      80
Partitioning      33
Peak height      166
Peak-height distribution      169
Peak-height fluctuations      167
Perfectly elastic      18
Periodic orbits      66 124
Persistent current      94
Phase relaxtion time      111
Phase space      28 82 185
Phase-coherent      132
Phase-interference terms      140
Phase-space average      139
Pitchfork bifurcation      150 154
Planck cell      69
Planck constant      41
Poincare sections      163
Poisson distribution      177
Porter - Thomas distribution      167
Power spectrum      5
Primitive periodic orbit      65 68 138
Problem of exponential proliferation      76
Propagator      61
Quantum antidots      130
Quantum billiards with lead wires      41
Quantum correction      102 140
Quantum dot      7 11
Quantum interference      100
Quantum wires      7
Radius of curvature      21
random matrix      176
Real-space representation      112
Reduced action      63
Retarded Green function      61 134
Saddle-point approximation      66
Saddle-point method      140
Scaling theory of localization      100
Scattering property of a billiard ball      17
Schr$\ddot{o}$dinger equation      41
Self-retracing orbit      107
Self-similar conductance fluctuations      123
Self-similar magneto-conductance fluctuations      120
Self-similar periodic orbits      127
Semiclassical approximation      10 14 48
Semiclassical Green function      63 169
Semiclassical Kubo formula      124
Semiclassical limit      55 62
Semiclassical path-integral expression      158
Semiclassical path-integral representation      103
Semiclassical propagator      63
Semiclassical quantization      60
Semiclassical theory      10
Semiclassical theory at finite temperatures      142
Sensitivity to initial conditions      18
Separatrices      82
Shannon information entropy      168
Shubnikov-de Haas oscillation      132 134 149
Sinai billiards      98 130
Single Sinai billiards      120
Skipping orbit      80
Small-angle induced diffraction      112
Soft-wall boundary      125
Soft-wall potential      149
Spherical Bessel function      91
Spherical shell      86 89
Spin degree of freedom      72
Spin factor      72
Square antidot lattices      146
Square superlattice      130
Stability matrix      68
Stadium      6 98
Stadium-shaped billiard table      7
Stationary states      41
Stationary-phase approximation      12 48 63
Statistical property of fluctuations      5
Superlattice      130
Symmetric gauge      134
Tangent bifurcations      150 154
Thermal cutoff length      75
Thermodynamic functions      76
Thermodynamics of mesoscopic systems      72
Three-dimensional (3-d) billiard      86 157
Time-reversal symmetric      101
Torus is resonant      65
Trace of Green function      61
Transmission amplitude      158
Transmission coefficient      15 52 157 159
Transmission components in $S$ matrix      112
Transversal curvature of saddle      127
Triangular antidot lattice      144 146
Triangular antidots      146
Tunneling contact      166
Two-dimensional (2-d) electron gas      7
Typical susceptibility      88
Uniform approximation      150
Universal area distribution      40
Universal quantity      72 88
Variational Principle      14
Vector potential      80
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