Mirror Symmetry (Clay Mathematics Monographs, V. 1)

Book Description

This thorough and detailed exposition is the result of an intensive month-long course sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives. The material will be particularly useful for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics.

This one-of-a-kind volume offers the first comprehensive exposition on this increasingly active area of study. It is carefully written by leading experts who explain the main concepts without assuming too much prerequisite knowledge. The book is an excellent resource for graduate students and research mathematicians interested in mathematical and theoretical physics.

Customer Reviews:

Detailed overview of the subject.......2005-05-16

Mirror symmetry has become an established branch of mathematics and mathematical physics, and research in the subject has resulted in brilliant developments. This sizable book contains essentially some (polished) lecture notes of a seminar series in mirror symmetry that was given in the spring of 2000. This reviewer only studied Part 5 of the book, entitled "Advanced Topics" and so only that part will be reviewed here. In addition, space constraints then dictate only a small portion of this part can be reviewed. Needless to say, any reader who intends to tackle this book will need a substantial background in modern mathematics and advanced physics, and a sizable commitment in time. The time spent is well worth it though, as both the mathematics and physics behind mirror symmetry has to rank as one of the most fascinating research topics in the last two decades.

In the chapter entitled "Topological Strings" the authors consider the functional integration of worldsheet geometries. This project involves essentially the integration over the complex structures of Riemann surfaces. Referring to this procedure as "quantum gravity", they do not address it in-depth, but instead focus on the coupling of topological sigma models to worldsheet gravity, which is called `topological string theory' in the literature. The authors first consider the case where the target is a Kahler manifold whose first Chern class is zero, since for this case the quantum cohomology ring is less easy to obtain, i.e. it can obtain contributions from holomorphic maps of any degree. Even for the case where there is no coupling to gravity, the degree 0 contribution is related to the classical intersection number. The contributions from higher degree result in the deformation of the classical cohomology ring into the quantum cohomology ring. The authors then ask whether there are any other correlators that will give nontrivial (non-zero) invariants in genus 0. Posing this question leads to the WDVV equation and the genus 0 topological string partition function. The n-point correlation functions of topological strings can then be defined as the nth partial derivatives of this function. For higher genus cases, the correlators are all zero, but the authors show the connection between the higher genus partition function and holomorphic anomalies. The case of three-dimensional Calabi-Yau manifolds is special, if one concentrates on the integration over the complex structures of the worldsheet. When the complex dimension of this moduli space is 3(g-1) then there are isolated points where holomorphic maps exist. Defining a topological string theory for Calabi-Yau threefolds is straightforward, as the author shows, and proceeds analogously to the case of topological field theory. A measure is defined on the moduli space of Riemann surfaces of genus g that cancels the axial charge anomaly. A genus g (>1) topological string amplitude, which is a section of a bundle over the moduli space of Calabi-Yau manifolds, is then obtained from this procedure. Modulo the presence of holomorphic anomalies, the authors show that the definition of topological string amplitudes is consistent with the topological symmetry. The origin of these holomorphic anomalies is discussed in fair detail by the authors, having their origin in the boundaries of the moduli space.

The rigorous mathematical formulation of mirror symmetry is of course of great interest to mathematicians. Because of its origin in string theory and quantum field theory, mirror symmetry has not yet received this kind of rigor. Chapters 37 and 38 of this book discuss some of the approaches that attempt to put mirror symmetry on a more rigorous foundation. One of these involves the use of `derived categories,' an approach that was recommended by the mathematician Maxim Kontsevich. The discussion in these chapters takes place in the context of D-branes, and Kontsevich conjectures that mirror symmetry is the equivalence of two categories: the derived category of coherent sheaves, and the category of Lagrangian submanifolds with flat U(1) connections. Specifically the equivalence entails the equivalence between the bounded derived category of coherent sheaves or `B-cycles' and the category of A-cycles with compositions defined in terms of holomorphic maps from disks. This latter category is derived from the Fukaya A-infinity category, as is shown by the authors. They discuss in detail this category, being essentially a generalization of a differential, graded algebra, especially how to obtain the compositions. In chapter 37, the authors give an explicit example of the equivalence of these categories for the case of the elliptic curve. The elliptic curve is interesting in this regard in that it is its own mirror, i.e. the complex parameter is mapped to the complexified Kahler parameter by the mirror map.

The derived category has sometimes been a stumbling block to those who want to understand the Kontsevich conjecture. The authors do not attempt to give the reader the needed insight into this kind of category, but merely take it to be a collection of all holomorphic bundles and coherent sheaves. Sheaves in this category can be subtracted from each other using a map between them. Physically, this subtraction corresponds to the annihilation of branes and anti-branes via a tachyon. Derived categories though are straightforward to think about if one views them from the standpoint of algebraic topology. Derived categories are rich enough to include notions of localization and triangulated objects (i.e. "complexes") and maps (i.e. morphisms) between these objects. This is a kind of "homology" but what is of main interest are homotopies between the morphisms. The class of homotopic morphisms between two complexes forms an abelian group and one can then obtain a category consisting of complexes as objects and classes of homotopic morphisms as morphisms. A cohomology functor can then be defined on this category, along with graded objects and differentials between them. The homotopic category can be given a "triangulation" and morphisms in this category that give rise to isomorphisms in cohomology are given special status, called `quasimorphisms.' The localization of this category with respect to quasimorphisms is called a derived category.

Exploring the Quantum: Atoms, Cavities, and Photons (Oxford Graduate Texts)

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Exploring the Quantum: Atoms, Cavities, and Photons (Oxford Graduate Texts)
Serge Haroche , and Jean-Michel Raimond
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Quantum Optics: An Introduction (Oxford Master Series in Physics, 6)
Introductory Quantum Optics
Quantum Physics
Quantum Field Theory
Atom-Photon Interactions: Basic Processes and Applications (Wiley Science Paperback Series)

ASIN: 0198509146

Book Description

The counter-intuitive aspects of quantum physics have been for long illustrated by thought experiments, from Einstein's photon box to Schrodinger's cat. These experiments have now become real, with single particles - electrons, atoms or photons - directly unveiling the weird features of the quantum. State superpositions, entanglement and complementarity define a novel quantum logic which can be harnessed for information processing, raising great hopes for applications. This book describes a class of such thought experiments made real. Juggling with atoms and photons confined in cavities, ions or cold atoms in traps, is here an incentive to shed a new light on the basic concepts of quantum physics. Measurement processes and decoherence at the quantum-classical boundary are highlighted. This volume, which combines theory and experiments, will be of interest to students in quantum physics, teachers seeking illustrations for their lectures and new problem sets, researchers in quantum optics and quantum information.

Aspects of Symmetry: Selected Erice Lectures

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A wonderful book to supplement one's QFT knowledge
A Classic
unconventional QFT book

Aspects of Symmetry: Selected Erice Lectures
Sidney Coleman
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
Lie Algebras in Particle Physics (Frontiers in Physics)
String Theory and M-Theory: A Modern Introduction
Field Theory : A Modern Primer (Frontiers in Physics Series, Vol 74)
Superstring Theory (Cambridge Monographs on Mathematical Physics)

ASIN: 0521318270

Book Description

This collection of review lectures on topics in theoretical high energy physics has few rivals for clarity of exposition and depth of insight. Delivered over the past two decades at the International School of Subnuclear Physics in Erice, Sicily, the lectures help to organize and explain material that a the time existed in a confused state, scattered in the literature. At the time they were given they spread new ideas throughout the physics community and proved very popular as introductions to topics at the frontiers of research.

Customer Reviews:

A wonderful book to supplement one's QFT knowledge.......2003-08-04

This 400-page book contains eight lectures of varying length (some are quite long). The first two are not very useful, but the remainder of the book is wonderful. It covers topics like scale invariance, Callan-Symanzik (RG) equations, renormalization theory (Hepp's theorem), spontaneously broken symmetries, classical and quantum solitons, instantons (in QM and in gauge theories), and 1/N expansion. These are all useful topics and must be understood by those in the field, and yet not all of them are covered by ordinary quantum field theory books like Peskin & Schroeder. The style is very friendly and readable and includes a lot of endnotes, appendices, and references. This book does not "read" like Peskin/Schroeder or Weinberg or Itzykson/Zuber; those books don't read. This one does. The equations are easy to follow and this book showcases the strength of Coleman's pedagogical style. In fact I can vouch that the tone and content of these lectures serves as a close substitue for Coleman's lectures themselves. The topics were all basically developed in the 1970s, and were themselves all quite hot research areas before supersymmetry and string theory revolutionized high-energy physics. However, the majority of this book is not an anachronism -- the renormalization group, spontaneously broken symmetries, solitons, instantons, and 1/N expansion all pervade modern physics.

A Classic.......2003-05-17

Coleman is one of the best field theorists and a great lecturer. His style in both research and lectures can be summarized as "turning obvious into trivial". Every topic is presented in the simplest possible way without loss of deep insights, which makes the book extremely comprehensible. The chapter on instantons is absolutely classic.

unconventional QFT book.......2000-04-13

Many physicists say that Coleman is one of the great field theoriest in time. This is the collection of what he had lectured. Each chapter has own its importance. The advantage of the book is that he avoided the mathematical complication to explain the real physics. It is very unique feature in the QFT books. So you can get the concept of field theory without mathematical jargon which most students hate.

Methods in Theoretical Quantum Optics (Oxford Series in Optical and Imaging Sciences)

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Review of "Methods in theoretical quantum optics"

Methods in Theoretical Quantum Optics (Oxford Series in Optical and Imaging Sciences)
Stephen M. Barnett , and Paul M. Radmore
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Modern Foundations Of Quantum Optics
Introductory Quantum Optics
Quantum Optics: An Introduction (Oxford Master Series in Physics, 6)
Fundamentals of Quantum Optics
Atom-Photon Interactions: Basic Processes and Applications (Wiley Science Paperback Series)

ASIN: 0198563620

Book Description

This book is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. It should be attractive to students who have already explored one of the more introductory texts such as Loudon's The quantum theory of light (2/e, 1983, OUP) and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.

Customer Reviews:

Review of "Methods in theoretical quantum optics".......2001-10-18

I find this book really excellent. It gives a masterly
written introduction to all the most fundamental mathematical
methods in quantum optics. The concepts are introduced very
carefully, all the passages are explained in full detail, and
the discussion is very thorough throghout the book.
The authors gradually and clearly introduce the main
mathematical objects always relating them to basic
interactions and physical situations.
Special care is dedicated to the discussion of the basic
quantum states, number, thermal, coherent and squeezed.
Atomic coherent states and multimode extensions are discussed
as well. In each instance, simple Hamiltonian models
giving rise to the fundamental quantum states are
introduced and analysed in detail; among others,
I find excellent the detailed analysis devoted to the Jaynes--Cummings model, the beam splitter,
and the squeezing Hamiltonian.
Quite a substantial part of the book is dedicated
to the discussion of the statistical properties of the
electromagnetic field, in particular the
characteristic functions
and their associated quasiprobability distributions.
I believe that this book will be very useful both as
an introductory textbook for graduate and advanced
undergraduate students, as well as a reference book
for professionals working in the field of quantum optics
and basic quantum mechanics.

Classical and Quantum Computation (Graduate Studies in Mathematics)

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A clear, concise exposition
Complexity of algorithms.

Classical and Quantum Computation (Graduate Studies in Mathematics)
A. Yu. Kitaev , A. H. Shen , and M. N. Vyalyi
Manufacturer: Amer Mathematical Society
ProductGroup: Book
Binding: Paperback

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Quantum Computation and Quantum Information
Quantum Computing (Natural Computing Series)
Problems And Solutions in Quantum Computing And Quantum Information
Principles of Quantum Computation and Information - Vol.1: Basic Concepts
An Introduction to Quantum Computing

ASIN: 0821832298

Book Description

This book is an introduction to a new rapidly developing theory of quantum computing. It begins with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea of complexity of an algorithm. The second part of the book provides an exposition of quantum computation theory. It starts with the introduction of general quantum formalism (pure states, density matrices, and superoperators), universal gate sets and approximation theorems. Then the authors study various quantum computation algorithms: Grover's algorithm, Shor's factoring algorithm, and the Abelian hidden subgroup problem. In concluding sections, several related topics are discussed (parallel quantum computation, a quantum analog of NP-completeness, and quantum error-correcting codes).

Rapid development of quantum computing started in 1994 with a stunning suggestion by Peter Shor to use quantum computation for factoring large numbers--an extremely difficult and time-consuming problem when using a conventional computer. Shor's result spawned a burst of activity in designing new algorithms and in attempting to actually build quantum computers. Currently, the progress is much more significant in the former: A sound theoretical basis of quantum computing is under development and many algorithms have been suggested.

In this concise text, the authors provide solid foundations to the theory--in particular, a careful analysis of the quantum circuit model--and cover selected topics in depth. Included are a complete proof of the Solovay-Kitaev theorem with accurate algorithm complexity bounds, approximation of unitary operators by circuits of doubly logarithmic depth. Among other interesting topics are toric codes and their relation to the anyon approach to quantum computing.

Customer Reviews:

A clear, concise exposition.......2007-04-09

I started off learning Quantum Computation and Quantum Information by reading Nielsen and Chuang's book in order to do research in my junior year on quantum cyptography. Despite the completeness and popularity of that book, it did not exhibit enough explanation and insights for me to be truly satisfied that quantum computation will truly take flight one day to be implementable in place of classical computation.

Recently, in my preparation for my qualifying exam in Quantum information at MIT, I commenced reading this book. The feeling was like drinking a long cool sip of water after a 10 mile run. In particular, I really like the mathematical rigor of the writers. I have known Kitaev as a clear and careful presentator while I was at CalTech as an undergrad, and this is clearly reflected in his book. I definitely would recommend this book to anyone interested in Quantum computing and quantum information, professionally or amateurishly to buy this book (and no, I was not bribed to give this review in order to pass my quals!).

Complexity of algorithms........2002-08-31

The book covers classical and quantum algorithms;-- of the 250 or so, pages of text, roughly the first 50 pages are "classical", the rest quantum;-- and indeed the aim of the book is to teach the wonders of the qubit-algorithms. While other books, such as Nielsen-Chuang, serve as (more or less)comprehensive references, the present book (by Kitaev et al) is focussed on complexity. The mathematical prerequisits are minimal, but a reader with some understanding of basic ideas from CS, and from quantum theory (at the level of ch 1 in Nielsen-Chuang), will get more out of Kitaev et al. The book is a translation of a Russian 1999 original, but it is really well done, and nicely updated;-- for example, a handy appendix was added, covering elementary math terms that are used.
The book does a great job in explaining the fundamentals, both at the level of the *intuitive ideas*, as well as the mathematical proofs. The big question is why some qubit-algorithms (such as P Shor's factoring algorithm), are a lot better than classical counterparts(for example polynomial vs exponential), and a reader comes away with a good understanding of this in the end.

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The Theory of Open Quantum Systems
Heinz-Peter Breuer , and Francesco Petruccione
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback

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Problems And Solutions in Quantum Computing And Quantum Information
Principles of Quantum Computation and Information - Vol.1: Basic Concepts
The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
Decoherence and the Appearance of a Classical World in Quantum Theory
Lectures on Quantum Information (Physics Textbook)

ASIN: 0199213909

Book Description

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

Wave Motion (Texts in Applied Mathematics, No. 24)

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Excellent Overview of Basic Wave Theory
Wave Motion

Wave Motion (Texts in Applied Mathematics, No. 24)
J. Billingham , and A. C. King
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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An Introduction to the Mathematical Theory of Waves (Student Mathematical Library, V. 3)

ASIN: 0521634504

Book Description

Waves are a ubiquitous and important feature of the physical world, and, throughout history, it has been a major challenge to understand them. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as with fluid mechanics, elasticity, and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.

Customer Reviews:

Excellent Overview of Basic Wave Theory.......2002-06-28

This is book is a little strange but still very good. It could be thought of as a modern version of Lighthill's "Waves in Fluids". It first assumes that you are familiar with a pretty wide range of mathematical tools, and also that you have the necessary experience to handle long calculations. If you're comfortable with the method of stationary phase and contour integration but you've never studied acoustics or shocks, then this book is probably a worthwhile read. It's also good as an introduction to more advanced areas such as solitons, although the book by Johnson and Drazin (Solitons: An Introduction) is probably a better resource. I would have liked a chapter on waves of importance in geophysics though, such as internal gravity waves, Coriolis waves, and Rossby waves. It would have made the book an even better resource.

Wave Motion.......2001-09-15

This modern book has considerable breadth and depth, and is ideally suited as a reference text as well as a text for upper class under graduate and graduate courses. It treats acoustic waves, waves in elastic media, fluid dynamical waves, electromagnetic waves and more. The material is clearly presented, including excellent illustrations. At the same time, it is mathematically rigorous and thereby equally appropriate as a text for applied mathematics as well as engineering courses and study. Each of the book's twelve chapters ends with a set of homework problems, for which the authors have assembled a comprehensive well organized instructor's solution manual.

Lorentzian Wormholes: From Einstein to Hawking (AIP Series in Computational and Applied Mathematical Physics)

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Buy a used copy

Lorentzian Wormholes: From Einstein to Hawking (AIP Series in Computational and Applied Mathematical Physics)
Matt Visser
Manufacturer: American Institute of Physics
ProductGroup: Book
Binding: Paperback

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A First Course in String Theory
General Relativity
Black Holes and Time Warps: Einstein's Outrageous Legacy (Commonwealth Fund Book Program)

ASIN: 1563966530

Book Description

From H.G. Wells to Star Trek, audiences have been captivated by the notions of time travel, time warps, space warps, and wornholes. But science fiction is not the only realm where these concepts thrive. An active group of general relativists and quantum field theorists has produced a considerable body of serious (thought admittedly speculative) mathematical and physical analyses of the wormhole system. Now, with this fascinating book, readers can explore in depth the science behind the science fiction. Drawing on pivotal work by Einstein, Wheeler, Morris, Thorne, Hawking, and others, Matt Visser charts the development and current state of Lorentzian wormhole physics. Dr. Visser shows that by pushing established physical theories to their limits, it is possible to deduce the physical properties of such exotica as wormholes and time travel. The physical framework he uses is derived from one of the major research frontiers of modern theoretical physics: quantum gravity-the intersection of classical Einstein gravity and quantum field theory. Physicists, students of general relativity, cosmology, quantum physics, or any interested reader with a background in physics wil find this a provocative introduction to an exciting and active topic of ongoing research.

Customer Reviews:

Buy a used copy.......2002-01-22

Some of the words in this book have appeared in movies and science fiction stories, but in this book they take on a mathematical/scientific meaning, thanks to the efforts of the author. Although the concepts in the book are still far-removed from experimental verification, one must credit the author with writing of a book that may be standard reading in centuries to come. When reading the book, one can only hope that its ideas, or some similar to them, will eventually allow humans to traverse time and space routinely. The reader will need a strong background in general relativity and quantum field theory to really appreciate the book, but after reading it will obtain a solid understanding of what might be calle, in the words of the author, "non-boring" physics.

After a brief overview of general relativity and quantum field theory, the author devotes the first part of the book to the history of wormhole physics. I was surprised to learn that the study of wormholes goes as far back as 1916 in paper by the physicist L.Flamm. But it was the desire of A. Einstein and N. Rosen to build a geometrical model of an elementary particle that is finite and singularity-free that set the tone for the research that continues to this day. Their ideas are reviewed in detail, and the author shows that viewing elementary particles as they did predicts they have internal structure, contrary to experiment. The contributions of J.A. Wheeler, namely his interest in topological issues in general relativity, and his geon/spacetime foam ideas are discussed also. The role of wormhole physics in developing a quantum theory of gravity, via the quantization of weak field gravity and the subsequent appearance of gravitons is treated also. The author lists the things that be done with quantized linearized gravity and gives references for research that counters the idea of spacetime foam. "Back-of-the-envelope" calculations are given for the importance of quantum fluctuations in the gravitational field at Planckian scales. A very interesting, and critical discussion is given of topology changes of spacetime via quantum fluctuations. The author states (but does not prove) various theorems regarding the topology of spacetime if a Lorentz metric is put on it. These results are pretty restrictive in limiting the existence of certain topology changes, but as the author remarks, one can abandon the idea of spacetime being everywhere-Lorentzian if one gives up the strong equivalence principle, an idea he clearly is not comfortable with. Given his remarks, it is interesting to ask whether quantum fluctuations could force a violation of the strong equivalence principle. The author does consider the role of quantum tunneling in changing spacetime topology, but concludes that it is not a meaningful question. However, he does devote a brief paragraph to the consideration of an energy-dependent effective topology which is the one of relevance to physics. Based on the "quantum claustrophobia" effect arising from the tendency of a particle to avoid small regions (i.e Heisenberg uncertainty), some regions of spacetime may thus not be visible from a quantum point of view. The author gives one example of this, but this idea has far-reaching consequences: not just for physics but for mathematics. If viewed from a quantum perspective, many of the usual mathematical structures in topology and other areas of mathematics are changed considerably. One can then perform a kind of interpolation between "quantum" and "classical" mathematical constructions.

The author switches to more modern developments in part 3, with the idea of a traversable wormhole due to M. S. Morris and K.S. Thorne leading off the discussion. These wormholes are shown to violate the weak, strong, and dominant energy conditions, implying the existence of negative energy density near the throat of the wormhole. The existence of this energy will remind the reader of the Casimir effect, and the author does discuss this effect in detail. In addition, the thin shell formalism is discussed as a tool to analyze traversable wormholes without spherical geometry. Global techniques and the topological censorship are used to give a mathematically precise definition of a traversable wormhole, although the censorship theorem is not proven.

Part 4 attempts to remove the idea of time travel from pure fantasy science fiction and give it more of a scientific foundation. The author is convincing in his efforts, via his thorough analysis of causality conditions in spacetime, and the explicit constructions of simple time machines, which in the author's words are a consequence of general relativity being "infested" with geometries that produce them. The van Stockum, Godel, Kerr, and Gott tiem machines are discussed in detail, and the author shows explicitly how to construct time machines via wormholes. He also addresses the problems that arise in the actual construction of these time machines, such as the possibility of a non-Hausdorff topology, the problem of unique histories (Novikov conjecture), the breakdown of unitarity in the quantum realm, and the Hawking chronology protection conjecture.

Section 5 is an overview of the quantum field theory needed for a study of wormhole physics. The author shows that time- and space-orientable spacetimes are incompatible with the Standard model. He discusses in detail the result that the ANEC condition can be violated by scale anomalies. Readers will have to have a very detailed knowledge of quantum field theory in curved spacetime to follow the discussion. The calculation of van Vleck determinants, familiar as Green function techniques, are done also. The stress-energy tensor is calculated explictly for traversable wormhole spacetimes. The Wheeler-DeWitt minisuperspace formalism is used to shed light on the quantum aspects of Lorentzian wormholes, and the Wheeler-DeWitt equation for Einstein gravity on minisuperspace is solved exactly.

Book Description

Explore the relationship between quantum mechanics and information-age applications
This volume takes an altogether unique approach to quantum mechanics. Providing an in-depth exposition of quantum mechanics fundamentals, it shows how these concepts are applied to most of today's information technologies, whether they are electronic devices or materials. No other text makes this critical, essential leap from theory to real-world applications.
The book's lively discussion of the mathematics involved fits right in with contemporary multidisciplinary trends in education: Once the basic formulation has been derived in a given chapter, the connection to important technological problems is summarily described. The many helpful features include
* Twenty-eight application-oriented sections that focus on lasers, transistors, magnetic memories, superconductors, nuclear magnetic resonance (NMR), and other important technology-driving materials and devices
* One hundred solved examples, with an emphasis on numerical results and the connection between the physics and its applications
* End-of-chapter problems that ground the student in both fundamental and applied concepts
* Numerous figures and tables to clarify the various topics and provide a global view of the problems under discussion
* Over two hundred illustrations to highlight problems and text
A book for the information age, Quantum Mechanics: Fundamentals and Applications to Technology promises to become a standard in departments of electrical engineering, applied physics, and materials science, as well as physics. It is an excellent text for senior undergraduate and graduate students, and a helpful reference for practicing scientists, engineers, and chemists in the semiconductor and electronic industries.

Customer Reviews:

Great for EE or MSE students.......2006-02-06

This book is easy to read. It is written by a professor in the EE Department at the University of Michigan. There are some technical applications of Quantum Mechanics. I strongly recommend to engineering students who want to really understand solid state physics and quantum optics. This book is a good introduction.

Singh's Quantum Mechanics.......1997-11-18

This volume has indeed taken a very unique approach to quantum mechanics, and I liked it very much. However, a few things may need to be improved: 1) I have noted that a significant portion of this volume is clearly taken directly from the excellent Q.M. book of Schiff. It would be nice if the author could give a little bit more of his own explanations and insights to make the volume even more original and useful. 2) I felt that too little emphasis was given to the matrix approach to Q.M., making some materials difficult to follow when the matrix formulation is invoked. 3) The application sections really linked well Q.M. to real-life problems. Being a devices physicist myself, the topics of these application examples suited my taste well. However, some example details were simply too brief, turning them into a source of confusion rather than clarification (e.g. "Excitons in Semiconductors." More words should be said about the "Central cell nature..."). - S.C. Ph.D.

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers

Average customer rating:

A good book for introduction
An excellent introduction
A excellent introduction to chaos
fundamental, systematic
Good book!

Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers
Robert Hilborn
Manufacturer: Oxford University Press, USA
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ASIN: 0198507232

Book Description

Chaos and Nonlinear Dynamics introduces students, scientists, and engineers to the full range of activity in the rapidly growing field on nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models (including a derivation of the famous Feigenbaum numbers). It is the only book at this level to include the increasingly important field of pattern formation and a survey of the controversial questions of quantum chaos. Important tools such as Lyapunov exponents and fractal dimensions are treated in detail. With over 200 figures and diagrams, and analytic and computer exercises for every chapter, the book can be used as a course-text or for self-instruction. This second edition has been restructured to make the book even more useful as a course text:many of the more complex examples and derivations have been moved to appendices. The extensive collection of annotated references has been updated through January 2000 and now includes listings of World Wide Web sites at many of the major nonlinear dynamics research centers. From reviews on the 1/e: 'What has been lacking is a single book that takes the reader with nothing but a knowledge of elementary calculus and physics all the way to the frontiers of research in chaos and nonlinear dynamics in all its facets. [...] a serious student, teacher, or researcher would be delighted to have this book on the shelf as a reference and as a window to the literature in this exciting and rapidly growing new field of chaos.' J.C. Sprott, American Journal of Physics, September 19944 'I congratulate the author on having managed to write an extremely thorough, comprehensive, and entertaining introduction to the fascinating field of nonlinear dynamics. His book is highly self- explanatory and ideally suited for self-instruction. There is hardly any question that the author does not address in an exceptionally readable manner. [...] I strongly recommend it to those looking for a comprehensive, practical, and not highly mathematical approach to the subject.' E.A. Hunt, IEEE Spectrum, December 1994

Customer Reviews:

A good book for introduction.......2007-05-22

I have recently bought this book. I have been studying on evolution of the test particles in a particular planewave spacetimes, and I have realized that the system admits a non-integrable structure. I should investigate whether the particle motion emerges chaos or not. But, my knowledge on chaos was almost zero, before buying this book. Now, I am going to complete the full analysis of the book, and I am much more familiar to the concept of chaos. However, this book can be used for just begining. To proceed to the advanced problems you should look for other materials, especially to the articles about chaos. I advise this book as a first book to start chaos.
Dr. Izzet Sakalli

An excellent introduction.......2007-03-09

Covers the basics in an in-depth manner, and exposes the reader to a wide range of exciting problems in dynamical systems theory. THE book to start with if one is interested in chaos.

A excellent introduction to chaos.......2003-11-25

This is an accessible and readable introductory textbook on chaos and nonlinear dynamics. It focuses on the ideas behind the theory of chaos, rather than on the details of the mathematics which can sometimes hinder rather than help the reader gain real insight into the mechanisms of nonlinear systems.

By this I do not mean that the author skips over the required mathematics. The text is intended for people with a solid background in differential equations, and some familiarity with classical dynamical systems is also helpful if not completely necessary. I would say it is targeted for advanced undergraduate or beginning graduate students in the mathematical sciences, as well as scientists/engineers with no background in chaos theory. However he does not get bogged down in mathematics at the expense of physical insight. I have been studying the book on my own and have run into few problems in understanding the explanations.

The first chapter goes over 3 chaotic systems as a practical way of introducing the reader to various features of such systems. This provides a basis of practical experience to draw upon for the rest of the book, where the principles of chaos are examined in greater detail. The extensive references given in the book are a valuable addition that can be used to further explore the scientific literature. The references include journal papers as well as books, articles, and software for dynamical systems.

If you have the requisite mathematical background and want to learn the basics of chaos and nonlinear dynamics, I highly recommend this book.

fundamental, systematic.......2001-11-07

If you are looking for a textbook or reference on chaos theory, I recommend you to buy this book.

If you read other books, you will eventually comment,'chaos is something related to mathematics, very abstract, has nothing to do with my messy bedroom...'

But if you read this book, you will scream,'Great! I have figured out the richness of the nonlinear world. I understand the different dynamical routes to chaos. I know different quantifying methods with their pros and cons. Most fascinating is that chaos is related to pattern formation and self organization, which I consider them as another field of knowledge before. Also chaos may provide a new approach to quantum mechanics, a good news for those including me who do not believe in the parallel universe interpretation. By the way, I learnt a lot from this book!'

Good book!.......2000-08-05

If you want to get on into chaos, just read this book. I especially like the very wide scope of the subjects considered and the insight provided by the author in pattern formation or quantum chaos.

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