Quantum physics Books

Book SynopsisThis text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.

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Book Synopsis'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.Table of ContentsVolume 1: Classical Relativistic Field Theory: Kinematical Aspects; Classical Relativistic Field Theory: Dynamical Aspects; Relativistic Quantum Field Theory: Operator Methods; Nonrelativistic Quantum Mechanics: Functional Methods; Relativistic Quantum Field Theory: Functional Integral Methods; Quantum Field Theory at Nonzero Temperature; Volume 2: Symmetries and Canonical Formalism; Gauge Symmetries and Constrained Systems; Weyl Quantization; Anomalies in Quantum Field Theory; Noncommutative Geometry; Quantum Groups; Noncommutative Geometry and Quantum Groups.

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Book SynopsisEver since 1911, the Solvay Conferences have shaped modern physics. The 25th edition held in October 2011 in Brussels and chaired by David Gross continued this tradition and celebrated the first centennial of this illustrious series of conferences. The development and applications of quantum mechanics have always been the main threads in the history of the Solvay Conferences, hence the 25th Solvay conference gathered many of the leading figures working on a wide variety of profound problems in physics where quantum mechanical effects play a central role. The conference addressed some of the most pressing open questions in the field of physics.The proceedings contain the “rapporteur talks” which give a broad overview with unique insights by distinguished and renowned scientists. These lectures cover the seven sessions: “History and Reflections”, “Foundations of Quantum Mechanics and Quantum Computation”, “Control of Quantum Systems”, “Quantum Condensed Matter”, “Particles and Fields”, “Quantum Gravity and String Theory” and it ended with a general discussion attempting to arrive at a synthesis.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants — some of which quite lively and involving dramatically divergent points of view — have been carefully edited and are reproduced in full.Table of ContentsHistory and Reflections (M Henneaux, J Heilbron and M Gell-Mann); Foundations of Quantum Mechanics and Quantum Computation (A Aspect, A Leggett and J Preskill); Control of Quantum Systems (P Zoller, I Cirac and S Girvin); Quantum Condensed Matter (B Halperin and S Sachdev); Particles and Fields (H Georgi and F Wilczek); Quantum Gravity and String Theory (J Polchinski, J Maldacena and A Guth); General Discussion and Conclusions (D Gross, A Aspect, P Zoller, B Halperin, H Georgi and J Polchinski).

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Book SynopsisA decade after it was first published, this book remains the best textbook in this exciting field. This 10th anniversary edition includes an introduction from the authors setting the work in context. Containing a wealth of figures and exercises, it is ideal for courses on the subject.Trade Review'Ten years after its initial publication, 'Mike and Ike' (as it's affectionately called) remains the quantum computing textbook to which all others are compared. No other book in the field matches its scope: from experimental implementation to complexity classes, from the philosophical justifications for the Church-Turing Thesis to the nitty-gritty of bra/ket manipulation. A dog-eared copy sits on my desk; the section on trace distance and fidelity alone has been worth many times the price of the book to me.' Scott Aaronson, Massachusetts Institute of Technology'Quantum information processing has become a huge interdisciplinary field at the intersection of both, theoretical and experimental quantum physics, computer science, mathematics, quantum engineering and, more recently, even quantum metrology. The book by Michael Nielsen and Isaac Chuang was seminal in many ways: it paved the way for a broader, yet deep understanding of the underlying science, it introduced a common language now widely used by a growing community and it became the standard book in the field for a whole decade. In spite of the fast progress in the field, even after 10 years the book provides the basic introduction into the field for students and scholars alike and the 10th anniversary edition will remain a bestseller for a long time to come. The foundations of quantum computation and quantum information processing are excellently laid out in this book and it also provides an overview over some experimental techniques that have become the testing ground for quantum information processing during the last decade. In view of the rapid progress of the field the book will continue to be extremely valuable for all entering this highly interdisciplinary research area and it will always provide the reference for those who grew up with it. This is an excellent book, well written, highly commendable, and in fact imperative for everybody in the field.' Rainer Blatt, Universtität Innsbruck'My well-perused copy of Nielsen and Chuang is, as always, close at hand as I write this. It appears that the material that Mike and Ike chose to cover, which was a lot, has turned out to be a large portion of what will become the eternal verities of this still-young field. When another researcher asks me to give her a clear explanation of some important point of quantum information science, I breathe a sigh of relief when I recall that it is in this book - my job is easy, I just send her there.' David DiVincenzo, IBM T. J. Watson Research Center'If there is anything you want to know, or remind yourself, about quantum information science, then look no further than this comprehensive compendium by Ike and Mike. Whether you are an expert, a student or a casual reader, tap into this treasure chest of useful and well presented information.' Artur Ekert, Mathematical Institute, University of Oxford'Nearly every child who has read Harry Potter believes that if you just say the right thing or do the right thing, you can coerce matter to do something fantastic. But what adult would believe it? Until quantum computation and quantum information came along in the early 1990s, nearly none. The quantum computer is the Philosopher's Stone of our century, and Nielsen and Chuang is our basic book of incantations. Ten years have passed since its publication, and it is as basic to the field as it ever was. Matter will do wonderful things if asked to, but we must first understand its language. No book written since (there was none before) does the job of teaching the language of quantum theory's possibilities like Nielsen and Chuang's.' Chris Fuchs, The Perimeter Institute for Theoretical Physics'Nielsen and Chuang is the bible of the quantum information field. It appeared 10 years ago, yet even though the field has changed enormously in these 10 years - the book still covers most of the important concepts of the field.' Lov Grover, Bell Labs'Quantum Computation and Quantum Information, commonly referred to as 'Mike and Ike', continues to be a most valuable resource for background information on quantum information processing. As a mathematically-impaired experimentalist, I particularly appreciate the fact that armed with a modest background in quantum mechanics, it is possible to pick up at any point in the book and readily grasp the basic ideas being discussed. To me, it is still 'the' book on the subject.' David Wineland, National Institute of Standards and Technology, Boulder, ColoradoTable of ContentsPart I. Fundamental Concepts: 1. Introduction and overview; 2. Introduction to quantum mechanics; 3. Introduction to computer science; Part II. Quantum Computation: 4. Quantum circuits; 5. The quantum Fourier transform and its application; 6. Quantum search algorithms; 7. Quantum computers: physical realization; Part III. Quantum Information: 8. Quantum noise and quantum operations; 9. Distance measures for quantum information; 10. Quantum error-correction; 11. Entropy and information; 12. Quantum information theory; Appendices; References; Index.

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Book SynopsisWith examples and clear explanation throughout, this step-by-step approach makes quantum theory of plasmons accessible to readers without specialized training in theory. Jacak uses original research results to offer a fully analytical theory formulation suitable for further development and applications. The theory is focused on the Random Phase Approximation description of plasmons in metallic nano-structures, previously defined for bulk metal. Particular attention is paid to large damping of plasmons in nanostructures including electron scattering and Lorentz friction losses, quantum description of plasmon photovoltaic effect is presented and there is in-depth analysis of plasmon-polariton kinetics in metallic nano-chains. Suitable for students in the field of plasmonics, opto-electronics and photonics, and for researchers active in the field of photo-voltaics, opto-electronics, nano-plasmonics and nano-photonics. Also of help to researchers in soft plasmonics with applications to eleTable of Contents1. Introduction and description of contents; 2. Physics of metals{preliminaries; 3. Quasiclassical description of plasmons in bulk metal; 4. Plasmon excitations in nanometer-size metallic particles; 5. Damping of plasmons in metallic nanoparticles; 6. Plasmon photovoltaic effect; 7. Plasmon-induced enhancement of efficiency of solar cells modified by metallic nanoparticles: material dependence; 8. Numerical simulation of plasmon photo-effect; 9. Plasmon-polaritons in metallic nanoparticle chains; 10. Plasmon-polariton kinetics in metallic nano-chain located in absorbing surroundings; 11. Plasmons in finite spherical ionic systems; 12. Plasmon-polaritons in a chain of finite ionic systems-model of saltatory conduction in myelinated axons; Bibliography; Index.

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Book SynopsisThis book provides an itinerary to quantum mechanics taking into account the basic mathematics to formulate it. Specifically, it features the main experiments and postulates of quantum mechanics pointing out their mathematical prominent aspects showing how physical concepts and mathematical tools are deeply intertwined. The material covers topics such as analytic mechanics in Newtonian, Lagrangian, and Hamiltonian formulations, theory of light as formulated in special relativity, and then why quantum mechanics is necessary to explain experiments like the double-split, atomic spectra, and photoelectric effect. The Schrödinger equation and its solutions are developed in detail. It is pointed out that, starting from the concept of the harmonic oscillator, it is possible to develop advanced quantum mechanics. Furthermore, the mathematics behind the Heisenberg uncertainty principle is constructed towards advanced quantum mechanical principles. Relativistic quantum mechanics is finally considered.The book is devoted to undergraduate students from University courses of Physics, Mathematics, Chemistry, and Engineering. It consists of 50 self-contained lectures, and any statement and theorem are demonstrated in detail. It is the companion book of "A Mathematical Journey to Relativity", by the same Authors, published by Springer in 2020.Table of Contents1 Newtonian Mechanics, Lagrangians and Hamiltonians 151.1 Some Words about the Priciples of Newtonian Mechanics . . . . . . . . . . . . 151.2 The Mechanical Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3 Lagrangians and Euler-Lagrange Equations . . . . . . . . . . . . . . . . . . . . 211.4 The Mechanical Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.5 Hamiltonians and General Hamilton’s Equations . . . . . . . . . . . . . . . . . 271.6 Poisson’s Brackets in Hamiltonian Mechanics . . . . . . . . . . . . . . . . . . . 292 Can Light Be Described by Classical Mechanics? 332.1 Michelson-Morley Experiment and the Principles of Special Relativity . . . . . 332.2 Moving among Inertial Frames: Lorentz Transformations . . . . . . . . . . . . 382.3 Addition of Velocities: the Relativistic Formula . . . . . . . . . . . . . . . . . . 412.4 Einstein’s Rest Energy Formula: E=mc2 . . . . . . . . . . . . . . . . . . . . . 422.5 Relativistic Energy Formula: E2 = p2 c2 + m2 c4 . . . . . . . . . . . . . . . . . 442.6 Describing Electromagnetic Waves: Maxwell’s Equations . . . . . . . . . . . . . 442.7 Invariance under Lorentz Transformations and non-Invariance under Galilei’sTransformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Why Quantum Mechanics? 513.1 What Do We Think about the Nature of Matter . . . . . . . . . . . . . . . . . 513.2 Monochromatic Plane Waves - the One Dimensional Case . . . . . . . . . . . . 553.3 Young’s Double Split Experiment: Light Seen as a Wave . . . . . . . . . . . . . 603.4 The Plank-Einstein formula: E=hf . . . . . . . . . . . . . . . . . . . . . . . . . 643.5 Light Seen as a Corpuscle: Einstein’s Photoelectric Eect . . . . . . . . . . . . 693.6 Atomic Spectra and Bohr’s Model of Hydrogen Atom . . . . . . . . . . . . . . . 703.7 Louis de Broglie Hypothesis: Material Objects Exhibit Wave-like Behavior . . . 733.8 Strengthening Einstein’s Idea: The Compton Eect . . . . . . . . . . . . . . . . 754 Schrödinger’s Equations and Consequences 794.1 The Schrödinger’s Equations - the one Dimensional Case . . . . . . . . . . . . . 794.2 Solving Schrödinger Equation for the Free Particle . . . . . . . . . . . . . . . . 814.3 Solving Schrödinger Equation for a Particle in a Box . . . . . . . . . . . . . . . 824.4 Solving Schrödinger Equation in the Case of Harmonic Oscillator. The Quantified Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 The Mathematics behind the Harmonic Oscillator 915.1 Hermite Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2 Real and Complex Vector Structures . . . . . . . . . . . . . . . . . . . . . . . . 975.2.1 Finite Dimensional Real and Complex Vector Spaces, Inner Product,Norm, Distance, Completeness . . . . . . . . . . . . . . . . . . . . . . . 975.2.2 Pre-Hilbert and Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . . 1005.2.3 Examples of Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2.4 Orthogonal and Orthonormal Systems in Hilbert Spaces . . . . . . . . . 1095.2.5 Linear Operators, Eigenvalues, Eigenvectors and Schrödinger Equation . 1105.3 Again about de Broglie Hypothesis: Wave-Particle Duality and Wave Packets . 1155.4 More about Electron in an Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 1186 Understanding Heisenberg’s Uncertainty Principle and the Mathematicsbehind 1216.1 Wave Packets and Schrödinger Equation . . . . . . . . . . . . . . . . . . . . . . 1216.2 Wave Functions with Determined Momentum and Energy. Schrödinger’s Equationfor related Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.3 Gauss’ Wave Packet and Heisenberg Uncertainty Principle . . . . . . . . . . . . 1256.4 The Mathematics behind the Wave Packets: Fourier Series and Fourier Transforms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1307 Evolving to Quantum Mechanics Principles 1437.1 Operators in Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . 1437.2 The Conservation Law . . . . . . . . . . . . . . 1497.3 Similarities with Hamiltonian Formalism of Classical Mechanics . . . . . . . . 1537.4 (t; x) from a Wave Function to a Quantum State of a System. The Postulatesof Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1558 Consequences of Quantum Mechanics Postulates 1678.1 Ehrenfest’s Theorem and Consequences . . . . . . . . . . . . . . . . . . . . . . 1678.2 A Consequence of QM Postulates: Heisenberg’s General Uncertainty Principle . 1708.3 Dirac Notation and what a QM Experiment Is . . . . . . . . . . . . . . . . . . . 1758.4 Polarization of Photons in Dirac Notation . . . . . . . . . . . . . . . . . . . . . 1788.5 Electron Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1868.6 Revisiting the Harmonic Oscillator: the Ladder Operators . . . . . . . . . . . . 1978.7 Angular Momentum Operators in Quantum Mechanics . . . . . . . . . . . . . . 2058.8 Gradient and Laplace Operator in Spherical Coordinates. Revisiting the SchrödingerEquation, now in Spherical Coordinates. Legendre’s Polynomials and the SphericalHarmonics. The Hydrogen Atom and Quantum Numbers . . . . . . . . . . 2118.9 Pauli Matrices and Dirac Equation. Relativistic Quantum Mechanics . . . . . . 228

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Book SynopsisAt last, science and the soul shake hands. Writing in a style that is both lucid and charming, mischievous and profound, Dr. Amit Goswami uses the language and concepts of quantum physics to explore and scientifically prove metaphysical theories of reincarnation and immortality. In PHYSICS OF THE SOUL, Goswami helps you understand the perplexities of the quantum physics model of reality and the perennial beliefs of spiritual and religious traditions. He shows how they are not only compatible, but, also, provide essential support for each other. The result is a deeply broadened, exciting and enriched worldview that integrates mind and spirit into science."Dr. Amit Goswami is one of the most brilliant minds in the world of science. His insights into the relationship between physics and consciousness have deeply influenced my understanding, and I am deeply grateful to him. Physics of the Soul is both challenging and brilliant." -Deepak Chopra "...one of the most original contemporary thinkers and writers in the field of physics and consciousness. . . Goswami makes difficult concepts accessible and exciting." -Stanley Krippner

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Book SynopsisThis text on quantum mechanics begins by covering all the main topics of an introduction to the subject. It then concentrates on newer developments. In particular it continues with the perturbative solution of the Schrödinger equation for various potentials and thereafter with the introduction and evaluation of their path integral counterparts. Considerations of the large order behavior of the perturbation expansions show that in most applications these are asymptotic expansions. The parallel consideration of path integrals requires the evaluation of these around periodic classical configurations, the fluctuation equations about which lead back to specific wave equations. The period of the classical configurations is related to temperature, and permits transitions to the thermal domain to be classified as phase transitions.In this second edition of the text important applications and numerous examples have been added. In particular, the chapter on the Coulomb potential has been extended to include an introduction to chemical bonds, the chapter on periodic potentials has been supplemented by a section on the band theory of metals and semiconductors, and in the chapter on large order behavior a section has been added illustrating the success of converging factors in the evaluation of asymptotic expansions. Detailed calculations permit the reader to follow every step.

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Book SynopsisThe first comprehensive philosophical and historical account of the experimental foundations of Niels Bohr’s practice of physics.Trade Review"Perovic offers a novel and refreshingly unorthodox interpretation of Bohr's seminal contributions to quantum physics and their philosophical implications. Adopting a method of historically sensitive analysis, he argues convincingly that the great Dane came to his overarching hypotheses, including the complementarity principle, by inductive reasoning inherently based on experiments. He skillfully defends Bohr against the charges that his epistemological and methodological views were amateurish armchair philosophy. Perovic's book on Bohr's vision is recommendable from a scientific, historical, and philosophical perspective."--Helge Kragh, Niels Bohr Institute, University of CopenhagenTable of ContentsIntroduction Part 1: Preliminaries 2 From Laboratory to Theory 3 From Classical Experiments to Quantum Theory Part 2: Bohr’s Vision in Practice: the Old Quantum Theory 4 Spectral Lines, Quantum States, and a Master Model of the Atom 5 The Correspondence Principle as an Intermediary Hypothesis 6 Reception 7 The Scientific Moderator Part 3: Toward Quantum Mechanics 8 Quantum Corpuscles, Quantum Waves, and the Experiments 9 The Uncertainty Principle as an Intermediary Hypothesis 10 Metaphysical Principles and Heuristic Rules 11 New Formalisms and Bohr’s Atom 12 Complementarity Established and Applied Part 4: Aftermath 13 Bohr and the “Copenhagen Orthodoxy” 14 Bohr’s Response to the Einstein-Podolsky-Rosen Argument 15 The Mature Bohr and the Rise of Slick Theory and Theoreticians Acknowledgments Bibliography Index

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Book SynopsisTrade Review"Prominent philosopher-scientists, from Abner Shimony to Paul Teller, contribute articles (some revisions of seminal publications) detailing presumptions and ambiguities of quantum measurement, written especially for the nonspecialist. Some highlights include Mermin's powerful (and amusing) 'device' to highlight the 'paradox' of quantum correlations, Linda Wessels' thorough catalog of specific implicit 'axioms' of the discussion, and Cushing's prospective overview. Other gems, including some simplified models of Bell's arguments, and a range of ontological frameworks—from realism to 'holism'—make this an urgently recommended work for all colleges." —Choice"The papers collected here demonstrate how analytic philosophy of science should be done. Quantum mechanics may be mysterious in some of its aspects, but those who wish to peddle mysticism on the basis on quantum theory would do well to stay away from this excellent collection of philosophical essays." —Canadian Philosophical Reviews"These papers, collected from a 1986 conference focusing on John S. Bell's celebrated 1964 theorem, examine the philosophical issues posed by quantum theory. The book introduces Bell's theorem so that readers can understand the papers, but it is not a technical overview of the theorem or of quantum mechanics." —Science News

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Book SynopsisNEW YORK TIMES BESTSELLER ? An exhilarating tour of humanity''s next great technological achievement?quantum computing?which may supercharge artificial intelligence, solve some of humanity''s biggest problems, like global warming, world hunger, and incurable disease, and eventually illuminate the deepest mysteries of science, by the bestselling author ofThe God Equation. ? ?Expertly describes and rectifies common misconceptions about quantum computing. ?Science[Kaku''s] lucid prose and thought process make abundant sense of this technological turning point.? ?The New York Times Book ReviewThe runaway success of the microchip may finally be reaching its end. As shrinking transistors approach the size of atoms, the phenomenal growth of computational power inevitably collapses. But this change heralds the birth of a revolutionary new type of computer, one that calculates on atoms themselves.Quantum computers promise unprecedented gains in computing power, enabling advancements that could overturn every aspect of our daily lives. While the media has mainly focused on their startling potential to crack any known encryption method, the race is already on to exploit their incredible power to revolutionize industry. Automotive makers, medical researchers, and consulting firms are all betting on quantum computing to design more efficient vehicles, create life-saving new drugs, and streamline businesses. But this is only the beginning. Quantum computing could be used to decode the complex chemical processes needed to produce cheap fertilizers and unleash a second Green Revolution; create a super battery that will enable the Solar Age; or design nuclear fusion reactors to generate clean, safe, renewable energy. It may even unravel the fiendishly difficult protein folding that lies at the heart of as-yet-incurable diseases like Alzheimer?s, ALS, and Parkinson?s. Already, quantum computers are being put to work to help solve the greatest mystery in science?the origin of the universe.There is no single problem humanity faces that might not be addressed by quantum computers. With his signature clarity and enthusiasm, Dr. Michio Kaku, who has spent his entire professional life working on the quantum theory, tells the thrilling story of this exciting scientific frontier and the race to claim humanity?s future.

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Book SynopsisIn Resonances, Instability, and Irreversibility: The LiouvilleSpace Extension of Quantum Mechanics T. Petrosky and I. Prigogine Unstable Systems in Generalized Quantum Theory E. C. G. Sudarshan, Charles B. Chiu, and G. Bhamathi Resonances and Dilatation Analyticity in Liouville Space Erkki J. Brandas Time, Irreversibility, and Unstable Systems in QuantumPhysics E. Eisenberg and L. P. Horwitz Quantum Systems with Diagonal Singularity I. Antoniou and Z. Suchanecki Nonadiabatic Crossing of Decaying Levels V. V. and Vl. V. Kocharovsky and S. Tasaki Can We Observe Microscopic Chaos in the Laboratory? Pierre Gaspard Proton Nonlocality and Decoherence in Condensed Matter --Predictions and Experimental Results C. A. Chatzidimitriou-Dreismann We are at a most interesting moment in the history of science.Classical science emphasized equilibrium, stabilitTable of ContentsThe Liouville Space Extension of Quantum Mechanics (T. Petrosky& I. Prigogine). Unstable Systems in Generalized Quantum Theory (E. Sudarshan, etal.). Resonances and Dilation Analyticity in Liouville Space (E.Bandas). Time, Irreversibility and Unstable Systems in Quantum Physics (E.Eisenberg & L. Horwitz). Quantum Systems with Diagonal Singularity (I. Antoniou & Z.Suchanecki). Nonadiabatic Crossing of Decaying Levels (V. Kocharovsky, etal.). Can We Observe Microscopic Chaos in the Laboratory? (P. Gaspard) Proton Nonlocality and Decoherence in CondensedMatter-Predictions and Experimental Results (C.Chatzidimitriou-Dreismann). Indexes.

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Book Synopsis#1 NEW YORK TIMES BESTSELLER • The epic story of the greatest quest in all of science—the holy grail of physics that would explain the creation of the universe—from renowned theoretical physicist and author of The Future of the Mind and The Future of Humanity.When Newton discovered the law of gravity, he unified the rules governing the heavens and the Earth. Since then, physicists have been placing new forces into ever-grander theories. But perhaps the ultimate challenge is achieving a monumental synthesis of the two remaining theories—relativity and the quantum theory. This would be the crowning achievement of science, a profound merging of all the forces of nature into one beautiful, magnificent equation to unlock the deepest mysteries in science: What happened before the Big Bang? What lies on the other side of a black hole? Are there other universes and dimensions? Is time travel possible? Why are w

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Book SynopsisThe new experiments underway at the Large Hadron Collider at CERN in Switzerland may significantly change our understanding of elementary particle physics and, indeed, the universe. Suitable for first-year graduate students and advanced undergraduates, this textbook provides an introduction to the field.Trade Review"[T]he book is a valuable and important addition to libraries, personal and institutional. It would serve as an excellent textbook to students taking up research in elementary particle physics and also as a reference volume."--B. Ananthanarayan, Current Science

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Book SynopsisEmphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, this book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems.Trade Review"Praises in no way can do full justice to the strength and detail of Mahan's well crafted and superb nutshell book. I found the book fascinating, stimulating and convincing and one can easily observe that the book is bursting with intellectual energy and ambition. I am not a rated scientist but as a student and follower of science and scientific projects since the beginning of my academic career, I have come across several books of topical interest but this time I enjoyed Quantum Mechanics in A Nutshell as a whole for its intelligence and manner of treatment of topics. All said and done, it is a book that can be enjoyed by any science student interested in quantum mechanics."--Uwe C. Tauber, Current Engineering Practice "[A] comprehensive and up-to-date exploration of quantum mechanics."--Nature Physics "This book, in spite of 11 chapters densely written, consists of a quick and very readable presentation of basic principles and an impressive number of applications of quantum mechanics. It can be profitably used in courses for beginning, intermediate and, in some cases, advanced students of physics."--Valter Moretti, Zentralblatt MATHTable of ContentsPreface xi Chapter 1: Introduction 1 1.1 Introduction 1 1.2 Schrodinger's Equation 2 1.3 Eigenfunctions 4 1.4 Measurement 8 1.5 Representations 8 1.5.1 Schrodinger Representation 9 1.5.2 Heisenberg Representation 10 1.6 Noncommuting Operators 11 Chapter 2: One Dimension 14 2.1 Square Well 14 2.2 Linear Potentials 26 2.3 Harmonic Oscillator 29 2.4 Raising and Lowering Operators 34 2.5 Exponential Potential 39 2.5.1 Bound State 40 2.5.2 Continuum State 42 2.6 Delta-Function Potential 45 2.7 Number of Solutions 48 2.8 Normalization 49 2.8.1 Bound States 49 2.8.2 Box Normalization 50 2.8.3 Delta-Function Normalization 51 2.8.4 The Limit of Infinite Volume 54 2.9 Wave Packets 56 Chapter 3: Approximate Methods 62 3.1 WKBJ 62 3.2 Bound States by WKBJ 68 3.2.1 Harmonic Oscillator 71 3.2.2 Morse Potential 71 3.2.3 Symmetric Ramp 73 3.2.4 Discontinuous Potentials 74 3.3 Electron Tunneling 76 3.4 Variational Theory 77 3.4.1 Half-Space Potential 80 3.4.2 Harmonic Oscillator in One Dimension 82 Chapter 4: Spin and Angular Momentum 87 4.1 Operators, Eigenvalues, and Eigenfunctions 87 4.1.1 Commutation Relations 88 4.1.2 Raising and Lowering Operators 89 4.1.3 Eigenfunctions and Eigenvalues 90 4.2 Representations 95 4.3 Rigid Rotations 100 4.4 The Addition of Angular Momentum 102 Chapter 5: Two and Three Dimensions 108 5.1 Plane Waves in Three Dimensions 108 5.2 Plane Waves in Two Dimensions 112 5.3 Central Potentials 114 5.3.1 Central Potentials in 3D 114 5.3.2 Central Potential in 2D 118 5.4 Coulomb Potentials 119 5.4.1 Bound States 119 5.4.2 Confluent Hypergeometric Functions 121 5.4.3 Hydrogen Eigenfunctions 121 5.4.4 Continuum States 125 5.5 WKBJ 126 5.5.1 Three Dimensions 126 5.5.2 3D Hydrogen Atom 127 5.5.3 Two Dimensions 128 5.6 Hydrogen-like Atoms 130 5.6.1 Quantum Defect 131 5.6.2 WKBJ Derivation 132 5.6.3 Expectation Values 134 5.7 Variational Theory 134 5.7.1 Hydrogen Atom: n 1 135 5.7.2 Hydrogen Atom: l 1 136 5.7.3 Helium Atom 137 5.8 Free Particles in a Magnetic Field 143 5.8.1 Gauges 143 5.8.2 Eigenfunctions and Eigenvalues 144 5.8.3 Density of States 146 5.8.4 Quantum Hall Effect 147 5.8.5 Flux Quantization 150 Chapter 6: Matrix Methods and Perturbation Theory 157 6.1 H and H0 157 6.2 Matrix Methods 158 6.2.1 2 x 2 160 6.2.2 Coupled Spins 160 6.2.3 Tight-Binding Model 163 6.3 The Stark Effect 166 6.4 Perturbation Theory 170 6.4.1 General Formulas 170 6.4.2 Harmonic Oscillator in Electric Field 174 6.4.3 Continuum States 176 6.4.4 Green's Function 180 6.5 The Polarizability 181 6.5.1 Quantum Definition 182 6.5.2 Polarizability of Hydrogen 183 6.6 Van der Waals Potential 188 6.7 Spin-Orbit Interaction 194 6.7.1 Spin-Orbit in Atoms 195 6.7.2 Alkali Valence Electron in Electric Field 199 6.8 Bound Particles in Magnetic Fields 202 6.8.1 Magnetic Susceptibility 204 6.8.2 Alkali Atom in Magnetic Field 205 6.8.3 Zeeman Effect 207 6.8.4 Paschen-Back Effect 209 Chapter 7: Time-Dependent Perturbations 213 7.1 Time-Dependent Hamiltonians 213 7.2 Sudden Approximation 215 7.2.1 Shake-up and Shake-off 216 7.2.2 Spin Precession 218 7.3 Adiabatic Approximation 220 7.4 Transition Rates: The Golden Rule 222 7.5 Atomic Excitation by a Charged Particle 226 7.6 Born Approximation to Scattering 231 7.6.1 Cross Section 232 7.6.2 Rutherford Scattering 235 7.6.3 Electron Scattering from Hydrogen 236 7.7 Particle Decay 237 Chapter 8: Electromagnetic Radiation 244 8.1 Quantization of the Field 245 8.1.1 Gauges 246 8.1.2 Lagrangian 250 8.1.3 Hamiltonian 253 8.1.4 Casimir Force 256 8.2 Optical Absorption by a Gas 258 8.2.1 Entangled Photons 268 8.3 Oscillator Strength 269 8.4 Polarizability 273 8.5 Rayleigh and Raman Scattering 278 8.6 Compton Scattering 283 Chapter 9: Many-Particle Systems 288 9.1 Introduction 288 9.2 Fermions and Bosons 289 9.2.1 Two Identical Particles 290 9.3 Exchange Energy 291 9.3.1 Two-Electron Systems 291 9.3.2 Parahelium and Orthohelium 293 9.3.3 Hund's Rules 293 9.4 Many-Electron Systems 295 9.4.1 Evaluating Determinants 295 9.4.2 Ground-State Energy 297 9.4.3 Hartree-Fock Equations 299 9.4.4 Free Electrons 301 9.4.5 Pair Distribution Function 303 9.4.6 Correlation Energy 304 9.4.7 Thomas-Fermi Theory 304 9.4.8 Density Functional Theory 307 9.5 Second Quantization 309 9.5.1 Bosons 309 9.5.2 Fermions 312 9.6 Bose-Einstein Condensation 313 9.6.1 Noninteracting Particles 313 9.6.2 Off-Diagonal Long-Range Order 314 Chapter 10: Scattering Theory 320 10.1 Elastic Scattering 320 10.1.1 Partial Wave Analysis 323 10.1.2 Scattering in Two Dimensions 326 10.1.3 Hard-Sphere Scattering 328 10.1.4 Ramsauer-Townsend Effect 330 10.1.5 Born Approximation 332 10.2 Scattering of Identical Particles 333 10.2.1 Two Free Particles 333 10.2.2 Electron Scattering from Hydrogen 335 10.3 T-Matrices 337 10.4 Distorted Wave Scattering 340 10.5 Scattering from Many Particles 343 10.5.1 Bragg Scattering 343 10.5.2 Scattering by Fluids 344 10.5.3 Strong Scattering 346 10.6 Wave Packets 347 10.6.1 Three Dimensions 347 10.6.2 Scattering by Wave Packets 348 Chapter 11: Relativistic Quantum Mechanics 352 11.1 Four-Vectors 352 11.2 Klein-Gordon Equation 354 11.2.1 Derivation 354 11.2.2 Free Particle 354 11.2.3 Currents and Densities 355 11.2.4 Step Potential 356 11.2.5 Nonrelativistic Limit 356 11.2.6 -Mesonic Atoms 357 11.3 Dirac Equation 360 11.3.1 Derivation 361 11.3.2 Current and Charge Density 364 11.3.3 Gamma-Matrices 364 11.3.4 Free-Particle Solutions 366 11.3.5 Spin-Projection Operators 369 11.3.6 Scattering of Dirac Particles 371 11.4 Antiparticles and Negative Energy States 374 11.5 Spin Averages 377 11.6 Nonrelativistic Limit 379 11.6.1 First Approximation 379 11.6.2 Second Approximation 380 11.6.3 Relativistic Corrections for Hydrogenic States 382 11.7 Relativistic Interactions 384 11.7.1 Photon Green's Function 384 11.7.2 Electron Green's Function 387 11.7.3 Boson Exchange 387 11.8 Scattering of Electron and Muon 388 Index 397

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Book SynopsisSuitable for graduate students studying the interaction of optical fields with atoms, this book provides an introduction to the prototypical problems of radiation fields interacting with two- and three- level atomic systems.Trade Review"Berman and Malinovsky's book can be recommended to graduate students and workers transferring from other areas."--D.G.C. Jones, Contemporary Physics "This high-quality, well-written book is a fine addition to the literature of modern optics... The general style is lucid and entirely fitting for a textbook... In all, this is a splendid book and I am confident that it will be widely received with considerable enthusiasm."--David L. Andrews, Optics & Photonics NewsTable of ContentsPreface xv Chapter 1: Preliminaries 1 Chapter 2: Two-Level Quantum Systems 17 Chapter 3: Density Matrix for a Single Atom 56 Chapter 4: Applications of the Density Matrix Formalism 83 Chapter 5: Density Matrix Equations: Atomic Center-of-Mass Motion, Elementary Atom Optics, and Laser Cooling 99 Chapter 6: Maxwell-Bloch Equations 120 Chapter 7: Two-Level Atoms in Two or More Fields: Introduction to Saturation Spectroscopy 136 Chapter 8: Three-Level Atoms: Applications to Nonlinear Spectroscopy-Open Quantum Systems 159 Chapter 9: Three-Level Atoms: Dark States, Adiabatic Following, and Slow Light 184 Chapter 10: Coherent Transients 206 Chapter 11: Atom Optics and Atom Interferometry 242 Chapter 12: The Quantized, Free Radiation Field 280 Chapter 13: Coherence Properties of the Electric Field 312 Chapter 14: Photon Counting and Interferometry 339 Chapter 15: Atom-Quantized Field Interactions 358 Chapter 17: Optical Pumping and Optical Lattices 402 Chapter 18: Sub-Doppler Laser Cooling 422 Chapter 19: Operator Approach to Atom-Field Interactions: Source-Field Equation 453 Chapter 20: Light Scattering 474 Chapter 21: Entanglement and Spin Squeezing 492 References 506 Bibliography 507 Index 509

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Book SynopsisTrade Review"This text is another great example of the 'In a Nutshell' series of science books from Princeton University Press. . . . The book offers an abundance of worked out examples and many interesting end-of-chapter problems. This is a text that is obviously designed for the advanced undergraduate or graduate physics student--these groups of individuals will find the work an excellent introduction to the standard model." * Choice *Table of ContentsPreface for Instructors ix Acknowledgments xi Introduction xiii Table of Symbols xv 1 Special Relativity 1 1.1 Galileo 2 1.2 Vectors and Tensors 3 1.3 Foundations of Relativity 13 1.4 Spacetime 15 1.5 Relativistic Dynamics 19 2 Scalar Fields 24 2.1 The Principle of Least Action 25 2.2 Continuous Fields 29 2.3 The Klein-Gordon Equation 32 2.4 Which Lagrangians Are Allowed? 33 2.5 Complex Scalar Fields 35 3 Noether's Theorem 43 3.1 Conserved Quantities for Particles 44 3.2 Noether's First Theorem 46 3.3 The Stress-Energy Tensor 49 3.4 Angular Momentum 52 3.5 Electric Charge 53 3.6 Digression: Inflation 54 4 Symmetry 61 4.1 What Groups Are 62 4.2 Finite Groups 63 4.3 Lie Groups 66 4.4 SU(2) 70 4.5 SU(3) 74 5 The Dirac Equation 79 5.1 Relativity and Quantum Mechanics 80 5.2 Solutions to the Dirac Equation 86 5.3 The Adjoint Spinor 88 5.4 Coordinate Transformations 90 5.5 Conserved Currents 93 5.6 Discrete Transforms 97 5.7 Quantum Free-Field Theory 100 6 Electromagnetism 109 6.1 A Toy Model of Electromagnetism 109 6.2 Gauge Transformations 112 6.3 Interpreting the Electromagnetic Lagrangian 116 6.4 Solutions to the Classical Free Field 122 6.5 The Low-Energy Limit 123 6.6 Looking Forward 126 7 Quantum Electrodynamics 129 7.1 Particle Decay 130 7.2 Scattering 140 7.3 Feynman Rules for the Toy Scalar Theory 148 7.4 QED 153 8 The Weak Interaction 164 8.1 Leptons 165 8.2 Massive Mediators 168 8.3 SU(2) 171 8.4 Helicity 177 8.5 Feynman Rules for the Weak Interaction 180 9 Electroweak Unification 184 9.1 Leptons and Quarks 184 9.2 Spontaneous Symmetry Breaking 192 9.3 The Higgs Mechanism 195 9.4 Higgs-Fermion Interactions 199 9.5 A Reflection on Free Parameters 202 10 Particle Mixing 205 10.1 Quarks 207 10.2 Neutrinos 216 10.3 Neutrino Masses 222 11 The Strong Interaction 229 11.1 SU(3) 229 11.2 Renormalization 238 11.3 Asymptotic Freedom 245 12 Beyond the Standard Model 253 12.1 Free Parameters 253 12.2 Grand Unified Theories 255 12.3 Supersymmetry 259 12.4 The Strong CP Problem 264 12.5 Some Open Questions 266 Appendix A Spinors and c-Matrices 271 Appendix B Decays and Cross Sections 274 Appendix C Feynman Rules 277 Appendix D Groups 281 Bibliography 283 Index 291

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Book SynopsisTrade Review"Recommended."---E. Kincanon, CHOICE

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Book SynopsisTrade Review"Recommended."---E. Kincanon, CHOICE

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Book SynopsisThis book introduces contemporary cutting-edge research in quantum mechanics through problems and solutions based on topics rarely covered in the classroom. It is an indispensable resource for undergraduate and graduate students alike, as well as for instructors and early-career researchers in quantum mechanics, to complement traditional textbooks.

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Book SynopsisCategory theory reveals commonalities between structures of all sorts. This self-contained tour of applied category theory shows its potential in science, engineering, and beyond. Each chapter discusses a real-world application using category-theoretic tools, all of which are introduced in an accessible way with many examples and exercises.Trade Review'Category theory was always applied, but traditionally within pure mathematics. Now it is being used to clarify and synthesize a broad range of topics outside mathematics: from computer science to linguistics, from quantum theory to chemistry, and beyond. Charmingly informal yet crystal clear, Fong and Spivak's book does a wonderful job of demonstrating the power of category theory to beginners – even beginners without much background in pure mathematics.' John Baez, University of California, Riverside'The authors quite rightly describe category theory as a tool for thinking. So if your work requires thinking, this book is for you.' Bartosz Milewski, author of Category Theory for Programmers'This book provides a fantastic introduction to how category is not just abstract nonsense but can be applied to real-world engineering problems, pedagogical while still broad, and fun. A must read for all those entering the exciting emerging field of applied category theory by two key players of this community.' Bob Coecke, University of Oxford'An invitation to Applied Category Theory: Seven Sketches in Compositionality provides a grand tour of the fascinating emergent field of applied category theory that centers examples and use cases before gently introducing the accompanying abstract notions. Fong and Spivak should be congratulated for providing this accessible broad viewpoint to illustrate what category theory is all about vis-à-vis the real world.' Emily Riehl, The Johns Hopkins University'An Invitation to Applied Category Theory is clearly and entertainingly written, and provides a great entry into the world of applied category theory. It is chock full of concrete examples and illustrated with clear diagrams … Fong and Spivak will whet your appetite for learning about categories and how they - and the categorical way of thinking - can be applied in and beyond mathematics. And they will give you the means to do that in a self-contained text.' David Jaz Myers, MAA Reviews'Fong and Spivak's book is highly recommendable for anyone with even a passing interest in category theory in general. And it is mandatory reading for scholars aiming to apply category theory to real world problems.' Fernando A. Tohme, MathSciNet'The presentation is highly visual, employing graphs (nodes and edges), directed graphs, and hypergraphs. In addition, exercises intersperse each presentation, and the solutions to many of the exercises are included. Finally, the chapters include concluding summaries, with suggestions for further study. The book contains scores of references. In short, an excellent self-study resource for those interested in learning about applications of category theory to real-world problems.' J. T. Saccoman, Choice'… highly recommended.' Berthold Stoge, IUCr Journals CRYSTALLOGRAPHY JOURNALS ONLINETable of ContentsPreface; 1. Generative effects: orders and Galois connections; 2. Resource theories: monoidal preorders and enrichment; 3. Databases: categories, functors, and universal constructions; 4. Collaborative design: profunctors, categorification, and monoidal categories; 5. Signal flow graphs: props, presentations, and proofs; 6. Electric circuits: hypergraph categories and operads; 7. Logic of behavior: sheaves, toposes, and internal languages; Appendix. Exercise solutions; References; Index.

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Book SynopsisAdvanced research reference examining the closed and open quantum systems Control of Quantum Systems: Theory and Methods provides an insight into the modern approaches to control of quantum systems evolution, with a focus on both closed and open (dissipative) quantum systems.Table of ContentsAbout the Author xiii Preface xv 1 Introduction 1 1.1 Quantum States 2 1.2 Quantum Systems Control Models 3 1.2.1 Schrödinger Equation 4 1.2.2 Liouville Equation 4 1.2.3 Markovian Master Equations 5 1.2.4 Non-Markovian Master Equations 5 1.3 Structures of Quantum Control Systems 6 1.4 Control Tasks and Objectives 8 1.5 System Characteristics Analyses 9 1.5.1 Controllability 9 1.5.2 Reachability 9 1.5.3 Observability 10 1.5.4 Stability 10 1.5.5 Convergence 10 1.5.6 Robustness 10 1.6 Performance of Control Systems 11 1.6.1 Probability 11 1.6.2 Fidelity 11 1.6.3 Purity 12 1.7 Quantum Systems Control 13 1.7.1 Description of Control Problems 13 1.7.2 Quantum Control Theory and Methods 13 1.8 Overview of the Book 16 References 18 2 State Transfer and Analysis of Quantum Systems on the Bloch Sphere 21 2.1 Analysis of a Two-level Quantum System State 21 2.1.1 Pure State Expression on the Bloch Sphere 21 2.1.2 Mixed States in the Bloch Sphere 24 2.1.3 Control Trajectory on the Bloch Sphere 26 2.2 State Transfer of Quantum Systems on the Bloch Sphere 27 2.2.1 Control of a Single Spin-1/2 Particle 28 2.2.2 Situation with the Minimum Ωt of Control Fields 30 2.2.3 Situation with a Fixed Time T 31 2.2.4 Numerical Simulations and Results Analyses 33 References 37 3 Control Methods of Closed Quantum Systems 39 3.1 Improved Optimal Control Strategies Applied in Quantum Systems 39 3.1.1 Optimal Control of Quantum Systems 40 3.1.2 Improved Quantum Optimal Control Method 42 3.1.3 Krotov-Based Method of Optimal Control 43 3.1.4 Numerical Simulation and Performance Analysis 45 3.2 Control Design of High-Dimensional Spin-1/2 Quantum Systems 48 3.2.1 Coherent Population Transfer Approaches 48 3.2.2 Relationships between the Hamiltonian of Spin-1/2 Quantum Systems under Control and the Sequence of Pulses 49 3.2.3 Design of the Control Sequence of Pulses 52 3.2.4 Simulation Experiments of Population Transfer 53 3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems 57 3.3.1 Description of System Model 58 3.3.2 Geometric Control 59 3.3.3 Bang-Bang Control 61 3.3.4 Time Comparisons of Two Control Strategies 64 3.3.5 Numerical Simulation Experiments and Results Analyses 66 References 71 4 Manipulation of Eigenstates – Based on Lyapunov Method 73 4.1 Principle of the Lyapunov Stability Theorem 74 4.2 Quantum Control Strategy Based on State Distance 75 4.2.1 Selection of the Lyapunov Function 76 4.2.2 Design of the Feedback Control Law 77 4.2.3 Analysis and Proof of the Stability 78 4.2.4 Application to a Spin-1/2 Particle System 80 4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem 81 4.3.1 Description of the System Model 82 4.3.2 Optimal Control Law Design and Property Analysis 84 4.3.3 Simulation Experiments and the Results Comparisons 86 4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method 88 4.4.1 Mathematical Model 89 4.4.2 Realization of the Quantum Hadamard Gate 90 4.4.3 Design of Control Fields 92 4.4.4 Numerical Simulations and Comparison Results Analyses 94 References 96 5 Population Control Based on the Lyapunov Method 99 5.1 Population Control of Equilibrium State 99 5.1.1 Preliminary Notions 99 5.1.2 Control Laws Design 100 5.1.3 Analysis of the Largest Invariant Set 101 5.1.4 Considerations on the Determination of P 104 5.1.5 Illustrative Example 105 5.1.6 Appendix: Proof of Theorem 5.1 107 5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment 110 5.2.1 Design of Control Law 110 5.2.2 Convergence Analysis 113 5.2.3 Numerical Simulation on a Spin-1/2 System 114 5.3 Population Control of Eigenstates 117 5.3.1 System Model and Control Laws 117 5.3.2 Largest Invariant Set of Control Systems 118 5.3.3 Analysis of the Eigenstate Control 118 5.3.4 Simulation Experiments 119 References 123 6 Quantum General State Control Based on Lyapunov Method 125 6.1 Pure State Manipulation 125 6.1.1 Design of Control Law and Discussion 125 6.1.2 Control System Simulations and Results Analyses 129 6.2 Optimal Control Strategy of the Superposition State 131 6.2.1 Preliminary Knowledge 132 6.2.2 Control Law Design 133 6.2.3 Numerical Simulations 134 6.3 Optimal Control of Mixed-State Quantum Systems 135 6.3.1 Model of the System to be Controlled 136 6.3.2 Control Law Design 137 6.3.3 Numerical Simulations and Results Analyses 142 6.4 Arbitrary Pure State to a Mixed-State Manipulation 145 6.4.1 Transfer from an Arbitrary Pure State to an Eigenstate 146 6.4.2 Transfer from an Eigenstate to a Mixed State by Interaction Control 147 6.4.3 Control Design for a Mixed-State Transfer 149 6.4.4 Numerical Simulation Experiments 151 References 154 7 Convergence Analysis Based on the Lyapunov Stability Theorem 155 7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function 155 7.1.1 System Model and Control Design 155 7.1.2 Correspondence between any Target Eigenstate and the Value of the Lyapunov Function 156 7.1.3 Invariant Set of Control Systems 157 7.1.4 Numerical Simulations 161 7.1.5 Summary and Discussion 164 7.2 A Convergent Control Strategy of Quantum Systems 165 7.2.1 Problem Description 165 7.2.2 Construction Method of the Observable Operator 166 7.2.3 Proof of Convergence 168 7.2.4 Route Extension Strategy 173 7.2.5 Numerical Simulations 174 7.3 Path Programming Control Strategy of Quantum State Transfer 176 7.3.1 Control Law Design Based on the Lyapunov Method in the Interaction Picture 177 7.3.2 Transition Path Programming Control Strategy 178 7.3.3 Numerical Simulations and Results Analyses 182 References 186 8 Control Theory and Methods in Degenerate Cases 187 8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error 187 8.1.1 Control Design 188 8.1.2 Convergence Proof 192 8.1.3 Relation between Two Lyapunov Functions 193 8.1.4 Numerical Simulation and Result Analysis 193 8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity 195 8.2.1 Control Law Design and Convergence Proof 195 8.2.2 Numerical Simulation and Result Analysis 199 8.3 Implicit Lyapunov Control for the Quantum Liouville Equation 200 8.3.1 Description of Problem 201 8.3.2 Derivation of Control Laws 202 8.3.3 Convergence Analysis 205 8.3.4 Numerical Simulations 209 References 211 9 Manipulation Methods of the General State 213 9.1 Quantum System Schmidt Decomposition and its Geometric Analysis 213 9.1.1 Schmidt Decomposition of Quantum States 214 9.1.2 Definition of Entanglement Degree Based on the Schmidt Decomposition 215 9.1.3 Application of the Schmidt Decomposition 216 9.2 Preparation of Entanglement States in a Two-Spin System 220 9.2.1 Construction of the Two-Spin Systems Model in the Interaction Picture 220 9.2.2 Design of the Control Field Based on the Lyapunov Method 223 9.2.3 Proof of Convergence for the Bell States 226 9.2.4 Numerical Simulations 227 9.3 Purification of the Mixed State for Two-Dimensional Systems 230 9.3.1 Purification by Means of a Probe 230 9.3.2 Purification by Interaction Control 232 9.3.3 Numerical Experiments and Results Comparisons 233 9.3.4 Discussion 234 References 235 10 State Control of Open Quantum Systems 237 10.1 State Transfer of Open Quantum Systems with a Single Control Field 237 10.1.1 Dynamical Model of Open Quantum Systems 237 10.1.2 Derivation of Optimal Control Law 238 10.1.3 Control System Design 241 10.1.4 Numerical Simulations and Results Analyses 242 10.2 Purity and Coherence Compensation through the Interaction between Particles 246 10.2.1 Method of Compensation for Purity and Coherence 247 10.2.2 Analysis of System Evolution 250 10.2.3 Numerical Simulations 253 10.2.4 Discussion 255 Appendix 10.A Proof of Equation 10.59 257 References 258 11 State Estimation, Measurement, and Control of Quantum Systems 261 11.1 State Estimation Methods in Quantum Systems 261 11.1.1 Background of State Estimation of Quantum Systems 262 11.1.2 Quantum State Estimation Methods Based on the Measurement of Identical Copies 262 11.1.3 Quantum State Reconstruction Methods Based on System Theory 267 11.2 Entanglement Detection and Measurement of Quantum Systems 268 11.2.1 Entanglement States 269 11.2.2 Entanglement Witnesses 271 11.2.3 Entanglement Measures 273 11.2.4 Non-linear Separability Criteria 277 11.3 Decoherence Control Based on Weak Measurement 278 11.3.1 Construction of a Weak Measurement Operator 279 11.3.2 Applicability of Weak Measurement 280 11.3.3 Effects on States 282 Appendix 11.A Proof of Normed Linear Space (A, ¡¬ • ¡¬) 286 References 287 12 State Preservation of Open Quantum Systems 291 12.1 Coherence Preservation in a Λ-Type Three-Level Atom 291 12.1.1 Models and Objectives 292 12.1.2 Design of Control Field 294 12.1.3 Analysis of Singularities Issues 297 12.1.4 Numerical Simulations 299 12.2 Purity Preservation of Quantum Systems by a Resonant Field 301 12.2.1 Problem Description 302 12.2.2 Purity Property Preservation 303 12.2.3 Discussion 306 12.3 Coherence Preservation in Markovian Open Quantum Systems 307 12.3.1 Problem Formulation 308 12.3.2 Design of Control Variables 311 12.3.3 Numerical Simulations 313 12.3.4 Discussion 315 Appendix 12.A Derivation of HC 316 References 317 13 State Manipulation in Decoherence-Free Subspace 321 13.1 State Transfer and Coherence Maintainance Based on DFS for a Four-Level Energy Open Quantum System 321 13.1.1 Construction of DFS and the Desired Target State 322 13.1.2 Design of the Lyapunov-Based Control Law for State Transfer 325 13.1.3 Numerical Simulations 326 13.2 State Transfer Based on a Decoherence-Free Target State for a Λ-Type N-Level Atomic System 328 13.2.1 Construction of the Decoherence-Free Target State 328 13.2.2 Design of the Lyapunov-Based Control Law for State Transfer 331 13.2.3 Numerical Simulations and Results Analyses 332 13.3 Control of Quantum States Based on the Lyapunov Method in Decoherence-Free Subspaces 336 13.3.1 Problem Description 336 13.3.2 Control Design in the Interaction Picture 338 13.3.3 Construction of P and Convergence Analysis 339 13.3.4 Numerical Simulation Examples and Discussion 345 References 348 14 Dynamic Decoupling Quantum Control Methods 351 14.1 Phase Decoherence Suppression of an n-Level Atom in Ξ;-Configuration with Bang-Bang Controls 351 14.1.1 Dynamical Decoupling Mechanism 352 14.1.2 Design of the Bang–Bang Operations Group in Phase Decoherence 355 14.1.3 Examples of Design 357 14.2 Optimized Dynamical Decoupling in Ξ-Type n-Level Atom 360 14.2.1 Periodic Dynamical Decoupling 361 14.2.2 Uhrig Dynamical Decoupling 361 14.2.3 Behaviors of Quantum Coherence under Various Dynamical Decoupling Schemes 362 14.2.4 Examples 365 14.2.5 Discussion 366 14.3 An Optimized Dynamical Decoupling Strategy to Suppress Decoherence 366 14.3.1 Universal Dynamical Decoupling for a Qubit 367 14.3.2 An Optimized Dynamical Decoupling Scheme 369 14.3.3 Simulation and Comparison 369 14.3.4 Discussion 375 References 378 15 Trajectory Tracking of Quantum Systems 381 15.1 Orbit Tracking of Quantum States Based on the Lyapunov Method 382 15.1.1 Description of the System Model 382 15.1.2 Design of Control Law 384 15.1.3 Numerical Simulation Experiments and Results Analysis 385 15.2 Orbit Tracking Control of Quantum Systems 389 15.2.1 System Model and Control Law Design 390 15.2.2 Numerical Simulation Experiments 391 15.3 Adaptive Trajectory Tracking of Quantum Systems 394 15.3.1 Description of the System Model 396 15.3.2 Control System Design and Characteristic Analysis 398 15.3.3 Numerical Simulation and Result Analysis 400 15.4 Convergence of Orbit Tracking for Quantum Systems 402 15.4.1 Description of the Control System Model 403 15.4.2 Control Law Derivation 404 15.4.3 Convergence Analysis 404 15.4.4 Applications and Experimental Results Analyses 411 References 416 Index 419

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Book Synopsis

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Book SynopsisUnravels Complex Problems through Quantum Monte Carlo MethodsClusters hold the key to our understanding of intermolecular forces and how these affect the physical properties of bulk condensed matter. They can be found in a multitude of important applications, including novel fuel materials, atmospheric chemistry, semiconductors, nanotechnology, and computational biology. Focusing on the class of weakly bound substances known as van derWaals clusters or complexes, Stochastic Simulations of Clusters: Quantum Methods in Flat and Curved Spaces presents advanced quantum simulation techniques for condensed matter.The book develops finite temperature statistical simulation tools and real-time algorithms for the exact solution of the Schrödinger equation. It draws on potential energy models to gain insight into the behavior of minima and transition states. Using Monte Carlo methods as well as ground state variational andTable of ContentsFundamentals. Atomic Clusters. Methods in Curved Spaces. Applications to Molecular Systems. Bibliography. Index.

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Book SynopsisNajmi's primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.Trade ReviewA complete, concise and clear exposition of the more traditional tools related to linear filtering. -- Davide Barbieri Mathematical Reviews Since their emergence in the last eighties and early nineties of the twentieth century, wavelets and other multi-scale transforms have become powerful signal and image processing tools. Najmi's book provides physicists and engineers with a clear and concise introduction to this fascinating field. -- Ignace Loris American Journal of PhysicsTable of ContentsList of TablesList of FiguresList of AcronymsPrefaceAcknowledgments1. Analysis in Vector and Function Spaces1.1. Introduction1.2. The Lebesgue Integral1.3. Discrete Time Signals1.4. Vector Spaces1.5. Linear Independence1.6. Bases and Basis Vectors1.7. Normed Vector Spaces1.8. Inner Product1.9. Banach and Hilbert Spaces1.10. Linear Operators, Operator Norm, the Adjoint Operator1.11. Reproducing Kernel Hilbert Space1.12. The Dirac Delta Distribution1.13. Orthonormal Vectors1.14. Orthogonal Projections1.15. Multi-Resolution Analysis Subspaces1.16. Complete and Orthonormal Bases in L2 (R)1.17. The Dirac Notation1.18. The Fourier Transform1.19. The Fourier Series Expansion1.20. The Discrete Time Fourier Transform1.21. The Discrete Fourier Transform1.22. Band-Limited Functions and the Sampling Theorem1.23. The Basis Operator in L2(R)1.24. Biorthogonal Bases and Representations in L2 (R)1.25. Frames in a Finite Dimensional Vector Space1.26. Frames in L2 (R)1.27. Dual Frame Construction Algorithm1.28. Exercises2. Linear Time-Invariant Systems2.1. Introduction2.2. Convolution in Continuous Time2.3. Convolution in Discrete Time2.4. Convolution of Finite Length Sequences2.5. Linear Time-Invariant Systems and the Z Transform2.6. Spectral Factorization for Finite Length Sequences2.7. Perfect Reconstruction Quadrature Mirror Filters2.8. Exercises3. Time, Frequency, and Scale Localizing Transforms3.1. Introduction3.2. The Windowed Fourier Transform3.3. The Windowed Fourier Transform Inverse3.4. The Range Space of the Windowed Fourier Transform3.5. The Discretized Windowed Fourier Transform3.6. Time-Frequency Resolution of theWindowed Fourier Transform3.7. The Continuous Wavelet Transform3.8. The Continuous Wavelet Transform Inverse3.9. The Range Space of the Continuous Wavelet Transform3.10. The Morlet, the Mexican Hat, and the Haar Wavelets3.11. Discretizing the Continuous Wavelet Transform3.12. Algorithm A' Trous3.13. The Morlet Scalogram3.14. Exercises4. The Haar and Shannon Wavelets4.1. Introduction4.2. Haar Multi-Resolution Analysis Subspaces4.3. Summary and Generalization of Results4.4. The Spectra of the Haar Filter Coefficients4.5. Half-Band Finite Impulse Response Filters4.6. The Shannon Scaling Function4.7. The Spectrum of the Shannon Filter Coefficients4.8. Meyer's Wavelet4.9. Exercises5. General Properties of Scaling and Wavelet Functions5.1. Introduction5.2. Multi-Resolution Analysis Spaces5.3. The Inverse Relations5.4. The Shift-Invariant Discrete Wavelet Transform5.5. Time Domain Properties5.6. Examples of Finite Length Filter Coefficients5.7. Frequency Domain Relations5.8. Orthogonalization of a Basis Set: b1 Spline Wavelet5.9. The Cascade Algorithm5.10. Biorthogonal Wavelets5.11. Multi-Resolution Analysis Using Biorthogonal Wavelets5.12. Exercises6. Discrete Wavelet Transform of Discrete Time Signals6.1. Introduction6.2. Discrete Time Data and Scaling Function Expansions6.3. Implementing the DWT for Even Length h0 Filters6.4. Denoising and Thresholding6.5. Biorthogonal Wavelets of Compact Support6.6. The Lazy Filters6.7. Exercises7. Wavelet Regularity and Daubechies Solutions7.1. Introduction7.2. Zero Moments of the Mother Wavelet7.3. The Form of H0(z) and the Decay Rate of F(?)7.4. Daubechies Orthogonal Wavelets of Compact Support7.5. Wavelet and Scaling Function Vanishing Moments7.6. Biorthogonal Wavelets of Compact Support7.7. Biorthogonal Spline Wavelets7.8. The Lifting Scheme7.9. Exercises8. Orthogonal Wavelet Packets8.1. Introduction8.2. Review of the Orthogonal Wavelet Transform8.3. Packet Functions for Orthonormal Wavelets8.4. Discrete Orthogonal Packet Transform of Finite Length Sequences8.5. The Best Basis Algorithm8.6. Exercises9. Wavelet Transform in Two Dimensions9.1. Introduction9.2. The Forward Transform9.3. The Inverse Transform9.4. Implementing the Two-Dimensional Wavelet Transform9.5. Application to Image Compression9.6. Image Fusion9.8. ExercisesBibliographyIndex

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Book SynopsisProviding a unified account of nonrelativistic quantum mechanics, Fundamentals of Quantum Mechanics covers the principles and formalism of quantum mechanics and the development and application of general techniques for the solution of quantum mechanical problems. The author has done everything possible to make the math in this book accessible.The book is divided into three parts. The first part provides the historical basis and mathematical foundations on nonrelativistic quantum theory. The physical systems considered in this part are mainly in one dimension. The second part covers the fundamentals of quantum theory in three dimensions. Many-particle systems, the motion of a particle in three dimensions, angular and spin momenta, interaction of a charged particle with external fields, and matrix mechanical formulation of quantum mechanics are discussed in this part. The third part contains the approximation methods used in quantum mechanics and scattering theory. Carefully designed to cover the entire topic, the book provides sufficient breadth and depth both to familiarize readers with the basic ideas and mathematical expressions of quantum mechanics and to form the basis for deeper understanding.Table of ContentsFundamentals and One-Dimensional Systems. Three-Dimensional Systems. Approximation Methods and Scattering Theory.

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Book SynopsisOne of the Top Selling Physics Books according to YBP Library ServicesSuitable for graduate students, experienced researchers, and experts, this book provides a state-of-the-art review of the non-relativistic theory of high-energy ion-atom collisions. Special attention is paid to four-body interactive dynamics through the most important theoretical methods available to date by critically analyzing their foundation and practical usefulness relative to virtually all the relevant experimental data.Fast ion-atom collisions are of paramount importance in many high-priority branches of science and technology, including accelerator-based physics, the search for new sources of energy, controlled thermonuclear fusion, plasma research, the earth’s environment, space research, particle transport physics, therapy of cancer patients by heavy ions, and more.These interdisciplinary fields are in need of knowledge about many cross sections and collisional rates for the analyzed fast ion-atom collisions, such as single ionization, excitation, charge exchange, and various combinations thereof. These include two-electron transitions, such as double ionization, excitation, or capture, as well as simultaneous electron transfer and ionization or excitation and the like—all of which are analyzed in depth in this book. Quantum Theory of High-Energy Ion-Atom Collisions focuses on multifaceted mechanisms of collisional phenomena with heavy ions and atoms at non-relativistic high energies.Table of ContentsBasic Notions and Main Observables in Scattering Problems. Requirements of the Theory for the Experiment. Continuous Spectrum and Eigen-Problems of Resolvents. Linear and Bilinear Functionals. Definition of a Quantum Scattering Event. The Adiabatic Theorem and the Abel Strong Limit. Non-Stationary and Stationary Scattering via Strong Limits. Scattering Matrix and Transition Matrix. Spectral Analysis of Operators. The Existence and Completeness of Møller Wave Operators. Four-Body Theories for Fast Ion-Atom Collisions. Perturbation Series with the Correct Boundary Conditions. The Dodd–Greider Series for Four-Body Collisions. Double Electron Capture. Simultaneous Transfer and Ionization. Single Electron Detachment. Single Electron Capture. Simultaneous Transfer and Excitation. Concluding Remarks and Outlooks. Index.

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