Quantum Chaos and Mesoscopic Systems

Mathematical Methods in the Quantum Signatures of Chaos by Norman E. Hurt

Publisher: Springer Netherlands in Dordrecht

Written in English
Cover of: Quantum Chaos and Mesoscopic Systems | Norman E. Hurt
Published: Pages: 335 Downloads: 840
Share This

Subjects:

  • Quantum theory,
  • Mathematics,
  • Global analysis,
  • Number theory

About the Edition

This is the first monograph to present a comprehensive treatment of the mathematical foundations of quantum chaos. Precise results in this area involve an exciting mixture of analytical number theory, zeta and L-functions, random matrix theory, scattering theory, the Selberg trace formula, and related global functional analysis. Many examples are presented including polygonal and standard billiards systems and models on the pseudosphere. The physics of both compact and finite volume systems are discussed, as well as systems in the presence of a magnetic field. Results on the spectra of Gutzwiller models for mesoscopic systems are discussed including questions of dissolving eigenvalues, simplicity of the spectra and exceptional eigenvalues. Relationships to isometric-isospectral questions in physics are discussed. Finally, applications of quantum chaos to recent results on mesoscopic physics are discussed, in particular transport properties in these devices. Starting from simple examples, the text leads the reader through the most recent work of Sarnak, Luo and coworkers on arithmetic chaos, Zelditch, Degli Esposti and coworkers on quantum ergodicity, Bleher and coworkers on integrable systems, Gutkin, Veech and coworkers on polygonal billiards, Sarnak, Phillips and coworkers on spectra of Gutzwiller models, Mueller and others on scattering theory, Berry, Keating, Steiner, Aurich, Bolte, Schmit, Bogomolny and coworkers on quantum chaos and Marcus Beenakker and coworkers on mesoscopic systems. Audience: This book will be of use to physicists, mathematicians, and engineers interested in quantum chaos and its applications to mesoscopic systems.

Edition Notes

Statementby Norman E. Hurt
SeriesMathematics and Its Applications -- 397, Mathematics and Its Applications -- 397
Classifications
LC ClassificationsT57-57.97
The Physical Object
Format[electronic resource] :
Pagination1 online resource (xv, 335 p.)
Number of Pages335
ID Numbers
Open LibraryOL27084030M
ISBN 109048148111, 9401587922
ISBN 109789048148110, 9789401587921
OCLC/WorldCa851369494

We consider the recently developed semiclassical analysis of the quantum mechanical spectral form factor, which may be expressed in terms of classically defiable properties. When applied to electrons whose classical behavior is diffusive, the results of earlier quantum mechanical perturbative derivations, which were developed under a different. For a recent review on quantum chaos in mesoscopic systems see, e.g: Semiclassical Theory of Mesoscopic Quantum Systems, (Springer Tracts in Modern Physics ()). Besides the electronic devices, mesoscopic optical systems are also investigated, in particular the propagation of light and the radiation characteristics in small resonant. Chaos only exists in nonlinear systems (at least for classical macroscopic systems; see sec. 6 for subtitles regarding quantum chaos). Nonlinearity appears to be a necessary condition for the stretching and folding mechanisms, so would seem to be a . The development of the supersymmetry technique has led to significant advances in the study of disordered metals and semiconductors. The technique has proved to be of great use in the analysis of modern mesoscopic quantum devices, but is also finding applications in a broad range of other topics, such as localization and quantum by:

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. UNESCO-EOLSS SAMPLE CHAPTERS FUNDAMENTALS OF PHYSICS - Introduction To Quantum Chaos - Denis Ullmo and Steven Tomsovic ©Encyclopedia of Life Support Systems (EOLSS) infinity. Another branch is an analysis of what the behaviors of linear wave equation solutions may be in a short wavelength or asymptotic limit.   The quantum phenomena of tunneling and interference show up not only in the microscopic world of atoms and molecules, but also in cold materials of the real world, such as metals and semiconductors. Though not fully macroscopic, such mesoscopic systems contain a huge number of particles, and the holistic nature of quantum mechanics becomes. Quantum nonlinear resonance and quantum chaos in Aharonov-Bohm oscillations in mesoscopic semiconductor rings. Physical Review B, Vol. 56, Issue. 16, p. A general introduction sets out the main features of chaos in quantum systems. this book provides an overview of this rapidly expanding field, and will be of great interest to.

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. This volume provides a comprehensive and highly accessible introduction to quantum chaos. It emphasizes both the experimental and theoretical aspects of quantum chaos, and includes a discussion of supersymmetry techniques. Theoretical concepts are developed clearly and illustrated by numerous experimental or numerical examples. The author also shares the first . Novel interference effects and a new quantum phase in mesoscopic systems P SINGHA DEO yand A M JAYANNAVAR National Center for Basic Sciences, JD Block, Sector III,SaltLake City, Calcutta India y Institute of Physics, Sachivalaya Marg, Bhubaneswar , India Email: [email protected]; [email protected] Abstract. The aim of this book is to present a statistical theory of wave scattering by complex systems -systems which have a chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or possess quenched randomness, as in the case of disordered conductors- with emphasis on mesoscopic fluctuations.

Quantum Chaos and Mesoscopic Systems by Norman E. Hurt Download PDF EPUB FB2

Quantum Chaos and Mesoscopic Systems Mathematical Methods in the Quantum Signatures of Chaos. Authors: Hurt, N.E. Free Preview. Quantum Chaos and Mesoscopic Systems Mathematical Methods in the Quantum Signatures of Chaos.

Authors (view affiliations) Norman E. Hurt; Book. 6 Citations; Search within book. Front Matter. Pages i-xv. PDF. Signatures of Quantum Chaos.

Norman E. Hurt. Pages Billiards: Polygonal and Others. Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos (Mathematics and Its Applications) th Edition by N.E. Hurt (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.

Cited by: 2. Get this from a library. Quantum chaos and mesoscopic systems: mathematical methods in the quantum signatures of chaos. [Norman Hurt] -- This is the first monograph to present a comprehensive treatment of the mathematical foundations of quantum chaos.

Precise results in this area involve an exciting mixture of analytical number. Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?"The correspondence principle states that classical mechanics is the classical limit of quantum.

"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 Quantum Chaos and Mesoscopic Systems book physics looking for an entree to issues in quantum dots, and those in quantum chaos interested in learning about this specific Cited by: born understanding quantum field theory, either, a subject of comparable di culty.

ChaosBook is an advanced textbook on the theory of classical, turbulent, stochastic and quantum chaotic systems on level of a 2nd year graduate statistical mechanics or quantum field theory course.

Approach it the way that suits you best. Get this from a library. Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos. [Norman E Hurt] -- This is the first monograph to present a comprehensive treatment of the mathematical foundations of quantum chaos.

Precise results in this area involve an exciting mixture of analytical number. Mesoscopic systems are extremely useful to study the interplay between the quantum and classical worlds, and at the same time Quantum Chaos studies can be used to test fundamental questions of Condensed Matter Physics, like disorder, decoherence, dissipation and many-body effects.

Thus, mesoscopic physics has a close connection to the fields of nanofabrication and nanotechnology. Devices used in nanotechnology are examples of mesoscopic systems. Three categories of new electronic phenomena in such systems are interference effects, quantum confinement effects and charging effects.

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.

We have organized the book to emphasize this importance, presenting a series of articles on models and different mesoscopic systems, followed by the microstructures where most of this research is concentrated. Contents: Models and Natural Systems: Chaos in Many Body Quantum Systems (C Presilla et al.).

Quantum Chaos and Quantum Dots Katsuhiro Nakamura and Takahisa Harayama Mesoscopic Physics and Nanotechnology. Bridges nonlinear science and nanotechnology.

Gives self-contained introduction to the semiclassical theory, an important theory in modern physics. Combines basic theory with topical issues. 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. Quantum wires and dots are expected also to be able to significantly improve optical devices such as lasers.

This book provides general reviews on various subjects of pure physics, device physics, and materials research concerning such quantum structures, starting with a general introduction of physics of mesoscopic systems.

In mesoscopic systems, symmetries are key points that allow to illuminate essential features of finite quantum systems (e.g., [19, 20]).

The basic goal of this paper is to elucidate the above. A review of coherent and collective quantum optical effects like superradiance and coherent population trapping in mesoscopic systems is presented. Various new physical realizations of these phenomena are discussed, with a focus on their role for electronic transport and quantum dissipation in coupled nano-scale systems like quantum by: Quantum conductance characteristics of a mesoscopic superconducting quantum point contact are studied under the effect of an electric field.

The conductance is computed by using the Landauer-Buttiker formula. The energy of the tunneled electrons is calculated by using a Monte-Carlo technique.

The obtained results show the following features: (1) The decrease of the Cited by: 1. Driven quantum systems, described by Hamiltonian where x(t) is a time dependent parameter, are of interest in mesoscopic physics (quantum dots), Author: Doron Cohen.

This book is a snapshot of the vision shared by outstanding scientists on the key theoretical and experimental issues in Mesoscopic Physics. Quantum properties of electrons in solid state devices and transport in semiconducting and superconducting low-dimensional systems, are discussed, as well as the basis of quantum computing (entanglement, noise decoherence and.

The problem of quantum chaos.- Semi-classical quantization of chaotic billiards.- Shastic scattering theory random-matrix models for fluctuations in microscopic and mesoscopic systems.- Atomic and molecular physics experiments in quantum chaology.- Topics in quantum chaos.- Dynamical localization in open quantum systems.

CONTENTS iii Stability of Poincar´e map cycles. 89 There goes the neighborhood. 90 r´esum´e 90 commentary 91 exercises 91 references Quantum Fluctuations in Mesoscopic Systems F.

Benatti1; 2, F. Carollo3, R. Floreanini H. Narnhofer4 1Dipartimento di Fisica, Universit a di Trieste, Trieste, Italy 2Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Trieste, Italy 3School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems.

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.

This book presents the statistical theory of complex wave scattering and quantum transport in physical systems which have chaotic classical dynamics, as in the case of microwave cavities and quantum dots, or which possess quenched randomness, as in the case of disordered conductors - with an emphasis on mesoscopic fluctuations.

We consider the recently developed semiclassical analysis of the quantum mechanical spectral form factor, which may be expressed in terms of classically defiable properties. When applied to electrons whose classical behavior is diffusive, the results of earlier quantum mechanical perturbative derivations, which were developed under a different set of assumptions, are.

Keeping track its rapid progress, this book provides a broad survey of the latest developments in the field. The focus is on statistics and dynamics of mesoscopic systems with special emphasis on topics like quantum chaos, localization, noise and fluctuations, mesoscopic optics and quantum transport in nanostructures.

Quantum chaos is concerned with establishing the relation between boxes P (chaotic systems) and Q (quantum systems). In establishing this relation, it is useful to introduce a concept called phase Author: Martin Gutzwiller.

INTRODUCTION TO QUANTUM CHAOS Denis Ullmo1 and Steven Tomsovic2 1LPTMS, Univ Paris-Sud, CNRS UMROrsay Cedex, France 2Department of Physics and Astronomy, Washington State University, Pullman, WA USA J Keywords: quantum chaos, random matrix theory, spectral statistics, Gutzwiller trace for-File Size: 2MB.

Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized physics. Both chaos theory and quantum mechanics have achieved a fairly large level of glamour in the eyes of the general Cited by: 2.

quantum mechanics. Therefore, in this book I shall investigate quantum transport in mesoscopic systems that are classically chaotic, showing the success and failure of theoretical trials to explain experimental issues.

My basic idea is as follows: Our inability to explain anomalous quantum.Ongoing developments in nanofabrication technology and the availability of novel materials have led to the emergence and evolution of new topics for mesoscopic research, including scanning-tunnelling microscopic studies of few-atom metallic clusters, discrete energy level spectroscopy, the prediction of Kondo-type physics in the transport properties of quantum dots, time Price: $The main topics are semiclassical methods, the interplay of chaos with tunneling and localization, and quantum chaos in scattering and dissipative systems.

The present volume introduces many of the basic ideas and techniques in this field which are necessary to master the more specialized original literature.