Quantum Chaos and Quantum Dots

Hardcover | December 15, 2003

byKatsuhiro Nakamura, Takahisa Harayama

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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 itsexploration 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 interpretquantum 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 fiveto 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.

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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 ba...

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.
Format:HardcoverDimensions:212 pages, 9.21 × 6.14 × 0.63 inPublished:December 15, 2003Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198525893

ISBN - 13:9780198525899

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Table of Contents

1. Quantum chaos and billiards2. Quantum transport and chaos in billiards3. Motion of a billiard ball4. Semiclassical theory of conductance fluctuations5. Semiclassical quantization and thermodynamics of mesoscopic systems6. Orbital diamagnetism and persistent current7. Quantum interference in single open billiards8. Linear response theory in semiclassical regime9. Orbital bifurcations, Arnold diffusion and Coulomb blockade10. Nonadiabatic transition, energy diffusion and generalized friction