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| Author | : N.E. Hurt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 350 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 9401587922 |
Download Quantum Chaos and Mesoscopic Systems Book in PDF, ePub and Kindle
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 | : N.E. Hurt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 362 |
| Release | : 1997-02-28 |
| Genre | : Mathematics |
| ISBN | : 9780792344599 |
Download Quantum Chaos and Mesoscopic Systems Book in PDF, ePub and Kindle
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 | : K. Nakamura |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 224 |
| Release | : 2006-04-11 |
| Genre | : Science |
| ISBN | : 0306471213 |
Download Quantum versus Chaos Book in PDF, ePub and Kindle
Quantum and chaos, key concepts in contemporary science, are incompatible by nature. This volume presents an investigation into quantum transport in mesoscopic or nanoscale systems which are classically chaotic and shows the success and failure of quantal, semiclassical, and random matrix theories in dealing with questions emerging from the mesoscopic cosmos. These traditional theories are critically analysed, and this leads to a new direction. To reconcile quantum with chaos and to restore genuine temporal chaos in quantum systems, a time-discrete variant of quantum dynamics is proposed. Audience:This book will be of interest to graduate students and researchers in physics, chemistry and mathematics, whose work involves fundamental questions of quantum mechanics in chaotic systems.
| Author | : Società italiana di fisica |
| Publisher | : IOS Press |
| Total Pages | : 548 |
| Release | : 2000 |
| Genre | : Science |
| ISBN | : 1614992282 |
Download New Directions in Quantum Chaos Book in PDF, ePub and Kindle
The rapid progress of the research field of quantum chaos and its applications called for a book that keeps students abreast of the new developments and at the same time provides a solid basis in subjects which form the canon of the field. This book discusses the following topics: Spectral statistics and their semiclassical interpretation in terms of the Gutzwiller trace formula, Quantum chaos and its applications in mesoscopic physics, Spectral statistics and conductance fluctuations and Quantum chaos in systems with many degrees of freedom. The book connects and continues past and present achievements and prepares the ground for a future full of intriguing and important developments.
| Author | : Klaus Richter |
| Publisher | : Springer |
| Total Pages | : 222 |
| Release | : 2013-10-03 |
| Genre | : Science |
| ISBN | : 9783662156506 |
Download Semiclassical Theory of Mesoscopic Quantum Systems Book in PDF, ePub and Kindle
This book describes manifestations of classical dynamics and chaos in the quantum properties of mesoscopic systems. During the last two decades mesoscopic physics has evolved into a rapidly progressing and exciting interdisciplinary field of physics. The first part of the book deals with integrable and chaotic classical dynamics with particular emphasis on the semiclassical description of spectral correlations, thermodynamic properties and linear response functions. The main part shows applications to prominent observables in the mesoscopic context.
| Author | : Pier A. Mello |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 428 |
| Release | : 2004 |
| Genre | : Science |
| ISBN | : 9780198525820 |
Download Quantum Transport in Mesoscopic Systems Book in PDF, ePub and Kindle
This text presents the statistical theory of wave scattering and quantum transport in complex - chaotic and disordered - systems.
| Author | : Katsuhiro Nakamura |
| Publisher | : |
| Total Pages | : 228 |
| Release | : 2004 |
| Genre | : Mesoscopic phenomena (Physics). |
| ISBN | : 9780198525899 |
Download Quantum Chaos and Quantum Dots Book in PDF, ePub and Kindle
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 | : Fritz Haake |
| Publisher | : Springer |
| Total Pages | : 659 |
| Release | : 2019-02-18 |
| Genre | : Science |
| ISBN | : 3319975803 |
Download Quantum Signatures of Chaos Book in PDF, ePub and Kindle
This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.
| Author | : W.Dieter Heiss |
| Publisher | : Springer |
| Total Pages | : 410 |
| Release | : 1992-12-14 |
| Genre | : Mathematics |
| ISBN | : |
Download Chaos and Quantum Chaos Book in PDF, ePub and Kindle
Until now the important concept of quantum chaos has remained somewhat ill defined. This volume tackles the ubiquitous borderline between classical andquantum mechanics, studying in particular the semiclassical limit of chaotic systems. The effects of disorder from dynamics and their relation to stochastic systems, quantum coherence effects in mesoscopic systems, and the relevant theoretical approaches are fruitfully combined in this volume. The major paradigms of what is called quantum chaos, random matrix theory and applications to condensed matter and nuclear physics are presented. Detailed discussions of experimental work with particular emphasis on atomic physics are included. The book is highly recommended for graduate-student seminars.
| Author | : Vladimir Zelevinsky |
| Publisher | : American Institute of Physics |
| Total Pages | : 306 |
| Release | : 2005-07-22 |
| Genre | : Science |
| ISBN | : |
Download Nuclei and Mesoscopic Physics Book in PDF, ePub and Kindle
The goal of the Workshop was to open the way for exchange of ideas between physicists working in different areas of quantum physics but studying the objects of mesoscopic nature which reveal important generic features and allow for similar approaches. Among these objects are complex nuclei, atoms and molecules, nanoscale condensed matter systems, atomic clusters, atoms in traps, prototypes of quantum computers etc. The Workshop WNMP-2004 was organized with the idea of bringing together researchers actively working on the multitude of mesoscopic problems in various areas and, through cross-fertilizing discussions, make an attempt to bridge the existing gaps, find a common language and clean the way for future collaborations. The topics of common interest included general features of mesoscopic systems; experimental, theoretical and computational methods used for their studies; coherent phenomena, such as superfluidity and superconductivity; many-body quantum chaos; marginally stable and open systems; phase transitions and thermodynamic properties (an exciting subject with contradictory opinions reflected in the Proceedings).
