Random Matrix Theory And Statistics Of Quantum Transport In Chaotic Cavities
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| Author | : Estelle Basor |
| Publisher | : Springer Nature |
| Total Pages | : 606 |
| Release | : 2023-01-01 |
| Genre | : Mathematics |
| ISBN | : 3031138511 |
This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.
| Author | : Yuli V. Nazarov |
| Publisher | : Cambridge University Press |
| Total Pages | : 591 |
| Release | : 2009-05-28 |
| Genre | : Science |
| ISBN | : 0521832462 |
Quantum transport is a diverse field, sometimes combining seemingly contradicting concepts - quantum and classical, conduction and insulating - within a single nanodevice. Quantum transport is an essential and challenging part of nanoscience, and understanding its concepts and methods is vital to the successful fabrication of devices at the nanoscale. This textbook is a comprehensive introduction to the rapidly developing field of quantum transport. The authors present the comprehensive theoretical background, and explore the groundbreaking experiments that laid the foundations of the field. Ideal for graduate students, each section contains control questions and exercises to check readers' understanding of the topics covered. Its broad scope and in-depth analysis of selected topics will appeal to researchers and professionals working in nanoscience.
| Author | : Pier A. Mello |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 428 |
| Release | : 2004 |
| Genre | : Science |
| ISBN | : 9780198525820 |
This text presents the statistical theory of wave scattering and quantum transport in complex - chaotic and disordered - systems.
| Author | : Matthew Wright |
| Publisher | : Cambridge University Press |
| Total Pages | : 285 |
| Release | : 2010-07-26 |
| Genre | : Science |
| ISBN | : 1139491547 |
Linear acoustics was thought to be fully encapsulated in physics texts of the 1950s, but this view has been changed by developments in physics during the last four decades. There is a significant new amount of theory that can be used to address problems in linear acoustics and vibration, but only a small amount of reported work does so. This book is an attempt to bridge the gap between theoreticians and practitioners, as well as the gap between quantum and acoustic. Tutorial chapters provide introductions to each of the major aspects of the physical theory and are written using the appropriate terminology of the acoustical community. The book will act as a quick-start guide to the new methods while providing a wide-ranging introduction to the physical concepts.
| Author | : Elizabeth S. Meckes |
| Publisher | : Cambridge University Press |
| Total Pages | : 225 |
| Release | : 2019-08-01 |
| Genre | : Mathematics |
| ISBN | : 1108317995 |
This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.
| Author | : Édouard Brezin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 519 |
| Release | : 2006-07-03 |
| Genre | : Science |
| ISBN | : 140204531X |
Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
| Author | : Giulio Casati |
| Publisher | : IOS Press |
| Total Pages | : 554 |
| Release | : 2000 |
| Genre | : Optoelectronics |
| ISBN | : 9784274903663 |
| 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 | : Y Arakawa |
| Publisher | : CRC Press |
| Total Pages | : 908 |
| Release | : 2002-09-30 |
| Genre | : Science |
| ISBN | : 9780750308564 |
An international perspective on recent research, Compound Semiconductors 2001 provides an overview of important developments in III-V compound semiconductors, such as GaAs, InP, and GaN; II-VI compounds, such as ZnSe and CdTe; and IV-IV compounds, such as SiC and SiGe. The book contains 139 papers arranged in chapters on electronic devices, optical devices, magnetic materials, novel systems, quantum transport, optical characterization, quantum nanostructures, and material growth and characterization. The content encompasses the development of optical and electronic devices based on nitride semiconductors as well as the steady advances in traditional topics like III-V-based electronic and optical devices, growth and processing, and characterization. The book also includes novel research trends in quantum structures, such as quantum wires and dots, and spintronics, which are very promising for future developments in nanotechnology. As the primary forum for research into these materials and their device applications, this resource is an essential reference for researchers working on compound semiconductors in semiconductor physics, device physics, materials science, chemistry, and electronic and electrical engineering.
| Author | : Christos H Skiadas |
| Publisher | : World Scientific |
| Total Pages | : 411 |
| Release | : 2010-01-13 |
| Genre | : Science |
| ISBN | : 9814465283 |
This volume contains a collection of papers suggested by the Scientific Committee that includes the best papers presented in the 2nd International Conference (CHAOS2009) on Chaotic Modeling, Simulation and Applications, that was held in Chania, Crete, Greece, June 1-5, 2009. The aim of the conference was to invite and bring together people working in interesting topics of chaotic modeling, nonlinear and dynamical systems and chaotic simulation.The volume presents theoretical and applied contributions on chaotic systems. Papers from several nonlinear analysis and chaotic fields are included and new and very important results are presented. Emphasis was given to the selection of works that have significant impact in the chaotic field and open new horizons to further develop related topics and subjects. Even more the selected papers are addressed to an interdisciplinary audience aiming at the broad dissemination of the theory and practice of chaotic modeling and simulation and nonlinear science.
