Quantum Chaos and Quantum Dots
Author | : Katsuhiro Nakamura |
Publisher | : |
Total Pages | : 0 |
Release | : 2004 |
Genre | : Mesoscopic phenomena (Physics) |
ISBN | : |
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Author | : Katsuhiro Nakamura |
Publisher | : |
Total Pages | : 0 |
Release | : 2004 |
Genre | : Mesoscopic phenomena (Physics) |
ISBN | : |
Author | : Katsuhiro Nakamura |
Publisher | : |
Total Pages | : 228 |
Release | : 2004 |
Genre | : Mesoscopic phenomena (Physics). |
ISBN | : 9780198525899 |
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.
Author | : Sven Aberg |
Publisher | : World Scientific |
Total Pages | : 286 |
Release | : 2001-10-09 |
Genre | : Science |
ISBN | : 9814490431 |
Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium.
Author | : Martin C. Gutzwiller |
Publisher | : Springer Science & Business Media |
Total Pages | : 445 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 1461209838 |
Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.
Author | : Karl-Fredrik Berggren |
Publisher | : World Scientific |
Total Pages | : 286 |
Release | : 2001 |
Genre | : Science |
ISBN | : 9810247117 |
Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium.
Author | : N.E. Hurt |
Publisher | : Springer Science & Business Media |
Total Pages | : 362 |
Release | : 1997-02-28 |
Genre | : Mathematics |
ISBN | : 9780792344599 |
4. 2 Variance of Quantum Matrix Elements. 125 4. 3 Berry's Trick and the Hyperbolic Case 126 4. 4 Nonhyperbolic Case . . . . . . . 128 4. 5 Random Matrix Theory . . . . . 128 4. 6 Baker's Map and Other Systems 129 4. 7 Appendix: Baker's Map . . . . . 129 5 Error Terms 133 5. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 133 5. 2 The Riemann Zeta Function in Periodic Orbit Theory 135 5. 3 Form Factor for Primes . . . . . . . . . . . . . . . . . 137 5. 4 Error Terms in Periodic Orbit Theory: Co-compact Case. 138 5. 5 Binary Quadratic Forms as a Model . . . . . . . . . . . . 139 6 Co-Finite Model for Quantum Chaology 141 6. 1 Introduction. . . . . . . . 141 6. 2 Co-finite Models . . . . . 141 6. 3 Geodesic Triangle Spaces 144 6. 4 L-Functions. . . . . . . . 145 6. 5 Zelditch's Prime Geodesic Theorem. 146 6. 6 Zelditch's Pseudo Differential Operators 147 6. 7 Weyl's Law Generalized 148 6. 8 Equidistribution Theory . . . . . . . . . 150 7 Landau Levels and L-Functions 153 7. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . 153 7. 2 Landau Model: Mechanics on the Plane and Sphere. 153 7. 3 Landau Model: Mechanics on the Half-Plane 155 7. 4 Selberg's Spectral Theorem . . . . . . . . . . . 157 7. 5 Pseudo Billiards . . . . . . . . . . . . . . . . . 158 7. 6 Landau Levels on a Compact Riemann Surface 159 7. 7 Automorphic Forms . . . . . 160 7. 8 Maass-Selberg Trace Formula 162 7. 9 Degeneracy by Selberg. . . . 163 7. 10 Hecke Operators . . . . . . . 163 7. 11 Selberg Trace Formula for Hecke Operators 167 7. 12 Eigenvalue Statistics on X . . . . 169 7. 13 Mesoscopic Devices. . . . . . . . 170 7. 14 Hall Conductance on Leaky Tori 170 7.
Author | : Katsuhiro Nakamura |
Publisher | : CUP Archive |
Total Pages | : 228 |
Release | : 1994-06-02 |
Genre | : Mathematics |
ISBN | : 9780521467469 |
Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.
Author | : Daniel Braun |
Publisher | : Springer |
Total Pages | : 139 |
Release | : 2003-07-01 |
Genre | : Science |
ISBN | : 3540409165 |
This overview of the state of the art of research in an exciting field mainly emphasizes the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems.
Author | : Hans-Jürgen Stöckmann |
Publisher | : Cambridge University Press |
Total Pages | : 386 |
Release | : 1999-10-13 |
Genre | : Science |
ISBN | : 0521592844 |
Discusses quantum chaos, an important area of nonlinear science.
Author | : Linda Reichl |
Publisher | : Springer Nature |
Total Pages | : 555 |
Release | : 2021-04-12 |
Genre | : Science |
ISBN | : 3030635341 |
Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.