Quantum Chaos and Quantum Dots
Seiten
2003
Oxford University Press (Verlag)
978-0-19-852589-9 (ISBN)
Oxford University Press (Verlag)
978-0-19-852589-9 (ISBN)
This book describes quantum chaos and quantum transport in microscopic billiards. Microscopic billiards are typical dynamical systems in which it is easy to see chaos classically and also to investigate effects of chaos on quantum phenomena. Owing to recent progress in microstructure fabrication technology, quantum chaos can now be studied experimentally rather than only as a sophisticated theory.
Dynamics of billiard balls and their role in physics have received wide attention since the monumental lecture by Lord Kelvin at the turn of the 19th century. 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 its 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.
Dynamics of billiard balls and their role in physics have received wide attention since the monumental lecture by Lord Kelvin at the turn of the 19th century. 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 its 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.
Katsuhiro Nakamura is Professor of Applied Physics at Osaka City University in Japan. Takahisa Harayama is Senior Researcher at ATR Adaptive Communications Research Laboratories, Kyoto, in Japan.
1. Quantum chaos and billiards ; 2. Quantum transport and chaos in billiards ; 3. Motion of a billiard ball ; 4. Semiclassical theory of conductance fluctuations ; 5. Semiclassical quantization and thermodynamics of mesoscopic systems ; 6. Orbital diamagnetism and persistent current ; 7. Quantum interference in single open billiards ; 8. Linear response theory in semiclassical regime ; 9. Orbital bifurcations, Arnold diffusion and Coulomb blockade ; 10. Nonadiabatic transition, energy diffusion and generalized friction
| Erscheint lt. Verlag | 1.3.2004 |
|---|---|
| Reihe/Serie | Mesoscopic Physics and Nanotechnology ; 3 |
| Zusatzinfo | numerous line drawings |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 160 x 241 mm |
| Gewicht | 500 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik | |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| Technik | |
| ISBN-10 | 0-19-852589-3 / 0198525893 |
| ISBN-13 | 978-0-19-852589-9 / 9780198525899 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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