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By Katsuhiro Nakamura

Dynamics of billiard balls and their function in physics have obtained extensive realization. Billiards can these days be created as quantum dots within the microscopic global permitting one to envisage the so-called quantum chaos, (i.e.: quantum manifestation of chaos of billiard balls). in reality, as a result of fresh development in complicated expertise, nanoscale quantum dots, similar to chaotic stadium and antidot lattices analogous to the Sinai Billiard, may be fabricated on the interface of semiconductor heterojunctions. This ebook starts off ite exploration of the impression of chaotic electron dynamics on ballistic quantum delivery in quantum dots with a difficult scan on resistance fluctuations for stadium and circle dots. through the textual content, significant realization is paid to the semiclassical conception which makes it attainable to interpret quantum phenomena within the language of the classical international. Chapters one to 4 are occupied with the effortless statistical equipment (curvature, Lyapunov exponent, Kolmogorov-Sinai entropy and break out rate), that are wanted for a semiclassical description of delivery in quantum dots. Chapters 5 to 10 speak about the topical topics within the box, together with the ballistic susceptible localization, Altshuler-Aronov-Spivak oscillation, partial time-reversal symmetry, continual present, Arnold diffusion and Coulomb blockade.

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P. Glicofridis, R. Ashoori, and M. Shayegan, 2000, Topographic Mapping of the Quantum Hall Liquid using a Few-Electron Bubble, Science 289, 90. Fisher, M. P. , and D. H. Lee, 1989, Phys. Rev. Lett. 63, 903. , and S. H. Shenker, 1979, Phase diagrams of lattice gauge theories with Higgs fields, Phys. Rev. D 19, 3682. , and C. King, 1989, Comm. Math. Phys. 126, 167. , and A. Zee, 1991, Nucl. Phys. B 364, 517. 213 Ginzburg, V. , and L. D. Landau, 1950, J. exp. theor. Phys. 20, 1064. , 1984, Phys.

50) 1 where α = 2π J/2g is the artificial fine structure constant. The mass of the charged boson m is 2 −1 (8tl ) . An artificial atom (a bound state of two positive and negative charged bosons) has an energy level spacing 14 mc2a α2 and a size of order 2/αmca . In the following, we will discuss one experiment that can detect some of the above properties in the 2D system. Let us assume the rotor carries an electric dipole moment. c. to the rotor. Such a coupling can create a pair of positive and negative charged bosons.

Kivelson, 1989, Phys. Rev. Lett. 62, 82.

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