Overview

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.

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9780198525899

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Microscopic billiards is the medium through which Nakamura (applied physics, Osaka City U.) and Harayama, a senior researcher with a communications company in Kyoto, introduce quantum chaos and quantum transport to students and scholars with little or no previous knowledge about classical chaos theory, which they generally downplay in favor of the semiclassical approach. The discussion is limited to ballistic microstructures like quantum dots and anti-dots, and neglects several essential themes of quantum chaos, but the analytic methods and the approximations they explain should be applicable to generic systems other than billiards. They have substantially rewritten and expanded their Japanese Quantum Chaos-On the State of Quantum Billiards published by Baifukan Publishing, Tokyo, in 2000. --SciTech Book News<br> Quantum Chaos and Quantum Dots...is an interesting review of some quantum-transport and related problems in solid-state systems. The text should prove useful in two categories of physicists: those in solid state physics looking for an entree to issues in quantum dots, and those in quantum chaos interested in learning about this specific application...It should definitely be useful for researchers, including those at the graduate level...It is a good addition to the still-small collection of books in the fascinating and wide-open field of quantum chaos. --The Industrial Physicist<br>

Microscopic billiards is the medium through which Nakamura (applied physics, Osaka City U.) and Harayama, a senior researcher with a communications company in Kyoto, introduce quantum chaos and quantum transport to students and scholars with little or no previous knowledge about classical chaos theory, which they generally downplay in favor of the semiclassical approach. The discussion is limited to ballistic microstructures like quantum dots and anti-dots, and neglects several essential themes of quantum chaos, but the analytic methods and the approximations they explain should be applicable to generic systems other than billiards. They have substantially rewritten and expanded their Japanese Quantum Chaos-On the State of Quantum Billiards published by Baifukan Publishing, Tokyo, in 2000. --SciTech Book News Quantum Chaos and Quantum Dots...is an interesting review of some quantum-transport and related problems in solid-state systems. The text should prove useful in two categ

Author Information

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.

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