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Quantum Theory of Materials
by Efthimios Kaxiras John D. JoannopoulosThis accessible new text introduces the theoretical concepts and tools essential for graduate-level courses on the physics of materials in condensed matter physics, physical chemistry, materials science and engineering, and chemical engineering. Topics covered range from fundamentals such as crystal periodicity and symmetry, and derivation of single-particle equations, to modern additions including graphene, two-dimensional solids, carbon nanotubes, topological states, and Hall physics. Advanced topics such as phonon interactions with phonons, photons and electrons, and magnetism, are presented in an accessible way, and a set of appendices reviewing crucial fundamental physics and mathematical tools makes this text suitable for students from a range of backgrounds. Students will benefit from the emphasis on translating theory into practice, with worked examples explaining experimental observations, applications illustrating how theoretical concepts can be applied to real research problems, and 242 informative full color illustrations. End-of chapter exercises are included for homework and self-study, with solutions and lecture slides for instructors available online.
The Quantum Theory of Nonlinear Optics
by Peter D. DrummondPlaying a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.
Quantum Theory of Scattering
by Takashi Ohmura Ta-You WuThis volume addresses the broad formal aspects and applications of the quantum theory of scattering in atomic and nuclear collisions. An encyclopedic source of pioneering work, it serves as a text for students and a reference for professionals in the fields of chemistry, physics, and astrophysics. The self-contained treatment begins with the general theory of scattering of a particle by a central field. Subsequent chapters explore particle scattering by a non-central field, collisions between composite particles, the time-dependent theory of scattering, and nuclear reactions. An examination of dispersion relations concludes the text. Numerous graphs, tables, and footnotes illuminate each chapter, in addition to helpful appendixes and bibliographies.
Quantum Theory of Solids (Master's Series in Physics and Astronomy)
by Eoin O'ReillyQuantum Theory of Solids presents a concisely-structured tour of the theory relating to chemical bonding and its application to the three most significant topics in solid state physics: semiconductors, magnetism, and superconductivity--topics that have seen major advances in recent years. This is a unique treatment that develops the concepts of quantum theory for the solid state from the basics through to an advanced level, encompassing additional quantum mechanics techniques, such as the variational method and perturbation theory. Written at the senior undergraduate/masters level, it provides an exceptional grounding in the subject.
Quantum Theory without Reduction,
by CiniQuantum theory offers a strange, and perhaps unique, case in the history of science. Although research into its roots has provided important results in recent years, the debate goes on. Some theorists argue that quantum theory is weakened by the inclusion of the so called "reduction of the state vector" in its foundations. Quantum Theory without Reduction presents arguments in favor of quantum theory as a consistent and complete theory without this reduction and as a theory capable of explaining all known features of the measurement problem. This collection of invited contributions defines and explores different aspects of this issue, bringing an old debate into a new perspective and leading to a more satisfying consensus about quantum theory. The book will be of interest to researchers in theoretical physics and mathematical physics involved in the foundations of quantum theory. Scientists, engineers, and philosophers interested in the conceptual problems of quantum theory will also find this work stimulating.
The Quantum Theory—Origins and Ideas: A Historical Primer for Physics Students (History of Physics)
by Carl S. HelrichThis book offers a fresh perspective on some of the central experimental and theoretical works that laid the foundations for today's quantum mechanics: It traces the theoretical and mathematical development of the hypotheses that put forward to explain puzzling experimental results; it also examines their interconnections and how they together evolved into modern quantum theory. Particular attention is paid to J.J. Thomson's atomic modeling and experiments at the Cavendish Laboratory, Max Planck's struggle to explain the experimental results of Heinrich Rubens and Ferdinand Kurlbaum, as well as the path leading from Louis de Broglie’s ideas to the wave theory of Erwin Schrödinger. Combining his experience in teaching quantum mechanics with his interest in the historical roots of the subject, the author has created a valuable resource for understanding quantum physics through its history, and a book that is appreciated both by working physicists and historians.
Quantum Thermodynamics and Optomechanics (Springer Theses)
by Juliette MonselThis thesis demonstrates the potential of two platforms to explore experimentally the emerging field of quantum thermodynamics that has remained mostly theoretical so far. It proposes methods to define and measure work in the quantum regime. The most important part of the thesis focuses on hybrid optomechanical devices, evidencing that they are proper candidates to measure directly the fluctuations of work and the corresponding fluctuation theorem. Such devices could also give rise to the observation of mechanical lasing and cooling, based on mechanisms similar to a heat engine. The final part of the thesis studies how quantum coherence can improve work extraction in superconducting circuits. All the proposals greatly clarify the concept of work since they are based on measurable quantities in state of the art devices.
Quantum Tools for Macroscopic Systems (Synthesis Lectures on Mathematics & Statistics)
by Fabio Bagarello Francesco Gargano Francesco OliveriThis book describes how complex systems from a variety of fields can be modeled using quantum mechanical ideas; from biology and ecology, to sociology and decision-making. Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a wide range of macroscopic systems both within and outside physics. The mathematical basis of these models is covered in detail, providing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. The authors present an essential resource for researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to complex systems in the social, biological or ecological sciences.Describes how complex systems from a variety of fields can be modeled using quantum mechanical ideasProvides insight into the dynamics of macroscopic systems and opens new interdisciplinary research frontiersIntroduces quantum tools needed for the analysis of the dynamical behavior of macroscopic systems
Quantum Transport: Atom to Transistor
by Supriyo DattaThis 2005 book presents a unique approach to the fundamentals of quantum transport, and is aimed at senior undergraduate and graduate students. Some of the most advanced concepts of non-equilibrium statistical mechanics are included and yet no prior acquaintance with quantum mechanics is assumed. Chapter 1 provides a description of quantum transport in elementary terms accessible to a beginner. The book then works its way from the hydrogen atom to nanostructures ending with a unified model for quantum transport along with illustrative examples showing how conductors evolve from the atomic to the ohmic regime (or from 'atom to transistor') as they get larger. Many numerical examples are used to provide concrete illustrations and the corresponding MATLAB codes are provided in the book. These codes, along with videostreamed lectures by the author, keyed to specific sections of the book, are available at the webpage for the book - under 'resources and solutions'.
Quantum Transport
by Yuli V. Nazarov Yaroslav M. BlanterQuantum transport is a diverse field, sometimes combining seemingly contradicting concepts - quantum and classical, conduction and insulating - within a single nanodevice. Quantum transport is an essential and challenging part of nanoscience, and understanding its concepts and methods is vital to the successful fabrication of devices at the nanoscale. This textbook, first published in 2009, is a comprehensive introduction to the rapidly developing field of quantum transport. The authors present the comprehensive theoretical background, and explore the groundbreaking experiments that laid the foundations of the field. Ideal for graduate students, each section contains control questions and exercises to check readers' understanding of the topics covered. Its broad scope and in-depth analysis of selected topics will appeal to researchers and professionals working in nanoscience.
Quantum Transport in Interacting Nanojunctions: A Density Matrix Approach (Lecture Notes in Physics #1024)
by Andrea Donarini Milena GrifoniThis book serves as an introduction to the growing field of quantum many-body transport in interacting nanojunctions. It delves into a theoretical approach based on a general density-matrix formulation for open quantum systems. In the book, relevant transport observables, like the current or its higher order cumulants, are obtained by evaluating quantum statistical averages. This approach requires the knowledge of the reduced density matrix of the interacting nanosystems. The formulation for addressing transport problems, based on the evolution of the reduced density operator in Liouville space, is highly versatile. It enables the treatment of charge and spin transport across various realistic nanostructures. Topics encompass standard Coulomb blockade, cotunneling phenomena in quantum dots, vibrational and Franck-Condon effects in molecular junctions, as well as many-body interference observed in double quantum dots or carbon nanotubes. Derived from lectures tailored for graduate and advanced students at the University of Regensburg in Germany, this book is enriched with exercises and step-by-step derivations.
Quantum Transport Theory
by Jorgen RammerQuantum Transport Theory is a comprehensive account of recent achievements in the understanding of disordered conductors. Chapters cover the density matrix description of nonequilibrium statistical mechanics and newer topics in the field of condensed matter physics, including: weak localization; destruction of electronic phase coherence in disordered conductors; electron-electron and electron-phonon interaction in dirty metals; scaling theory of localization; the self-consistent theory of localization; and mesoscopic physics. The diagrammatic technique for systems out of equilibrium is developed systematically, and is used to study quantum kinetic equations and linear response theory.
Quantum Transport Theory
by Jorgen RammerQuantum Transport Theory is a comprehensive account of recent achievements in the understanding of disordered conductors. Chapters cover the density matrix description of nonequilibrium statistical mechanics and newer topics in the field of condensed matter physics, including: weak localization; destruction of electronic phase coherence in disordered conductors; electron-electron and electron-phonon interaction in dirty metals; scaling theory of localization; the self-consistent theory of localization; and mesoscopic physics. The diagrammatic technique for systems out of equilibrium is developed systematically, and is used to study quantum kinetic equations and linear response theory.
Quantum Transport Theory
by Jorgen RammerQuantum Transport Theory is a comprehensive account of recent achievements in the understanding of disordered conductors. Chapters cover the density matrix description of nonequilibrium statistical mechanics and newer topics in the field of condensed matter physics, including: weak localization; destruction of electronic phase coherence in disordered conductors; electron-electron and electron-phonon interaction in dirty metals; scaling theory of localization; the self-consistent theory of localization; and mesoscopic physics. The diagrammatic technique for systems out of equilibrium is developed systematically, and is used to study quantum kinetic equations and linear response theory.
Quantum Triangulations
by Mauro Carfora Annalisa MarzuoliResearch on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Quantum Triangulations
by Annalisa Marzuoli Mauro CarforaResearch on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Quantum [Un]Speakables II
by Reinhold Bertlmann Anton ZeilingerThis self-contained essay collection is published to commemorate half a century of Bell's theorem. Like its much acclaimed predecessor "Quantum [Un]Speakables: From Bell to Quantum Information" (published 2002), it comprises essays by many of the worlds leading quantum physicists and philosophers. These revisit the foundations of quantum theory as well as elucidating the remarkable progress in quantum technologies achieved in the last couple of decades. Fundamental concepts such as entanglement, nonlocality and contextuality are described in an accessible manner and, alongside lively descriptions of the various theoretical and experimental approaches, the book also delivers interesting philosophical insights. The collection as a whole will serve as a broad introduction for students and newcomers as well as delighting the scientifically literate general reader.
The Quantum Universe: (And Why Anything That Can Happen, Does)
by Brian Cox Jeff ForshawThe world we live in is stranger than we can possibly imagine. The closest we've got to understanding it - so far - is with quantum physics. But what is quantum physics? And how, exactly, can it help us make sense of the universe?In The Quantum Universe, Brian Cox and Jeff Forshaw give us the real science behind the bizarre, wonderful, mind-boggling behaviour of the atoms and energy that make up the cosmos, and reveal just how everything that can happen, does happen. 'An engaging, ambitious and creative tour of our quantum universe. ' Guardian'Given that Einstein himself never quite got his head around the quantum universe, the task that the two professors have taken on - to demystify quantum physics - is not to be taken lightly . . . they do a great job. ' The Times'As breezily a written accessible account of the theory of quantum mechanics as you could wish for. ' Observer'The authors' love for their subject shines through the book. ' Economist
Quantum Untangling: An Intuitive Approach to Quantum Mechanics from Einstein to Higgs
by Simon SherwoodQuantum Untangling Non-technical and accessible primer providing key foundational knowledge on quantum mechanics and quantum field theory Quantum Untangling introduces the readers to the fascinating and strange realm of quantum mechanics and quantum field theory, written in an accessible manner while not shying away from using mathematics where necessary. The book goes into sufficient depth and conveys basic and more intricate concepts such as wave-particle duality, wave functions, the superposition principle, quantum tunneling, the quantum harmonic oscillator, the Dirac equation, and Feynman diagrams. It also covers the physics of the Higgs boson and provides a glimpse into string theory and loop quantum gravity. Overall, the author introduces complex concepts of quantum mechanics in an accessible and fun-to-read manner while laying the groundwork for mastering an advanced level of treatment in standard quantum mechanics textbooks and university courses. Quantum Untangling includes information on: Special relativity, time and length distortion, Einstein’s famous equation, how Einstein figured it out, and the implications for energy, mass and momentum Wave particle duality, discussing what classical physics cannot explain, quanta of light and the photoelectric effect, De Broglie’s crazy idea, and the double-slit experiment Making sense of Schrödinger’s equation, angular momentum and the wave function, angular rotational energy, atomic structure and molecular bonds Spin, Quantum Electrodynamics, gauge invariance, the strong and weak forces, plus a step-by-step description of the Higgs mechanism With Quantum Untangling, any reader with a good grasp of and an above-average interest in mathematics at advanced high-school level can follow the presentation and acquaint themselves with the fundamental and advanced topics of quantum mechanics and quantum field theory, making it a helpful resource for many different students.
Quantum Variational Calculus
by Agnieszka B. Malinowska Delfim F. M. TorresThis Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.
Quantum versus Classical Mechanics and Integrability Problems: towards a unification of approaches and tools
by Maciej BłaszakThis accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Quantum Walks and Search Algorithms (Quantum Science and Technology)
by Renato PortugalThe revised edition of this book offers an extended overview of quantum walks and explains their role in building quantum algorithms, in particular search algorithms.Updated throughout, the book focuses on core topics including Grover's algorithm and the most important quantum walk models, such as the coined, continuous-time, and Szedgedy's quantum walk models. There is a new chapter describing the staggered quantum walk model. The chapter on spatial search algorithms has been rewritten to offer a more comprehensive approach and a new chapter describing the element distinctness algorithm has been added. There is a new appendix on graph theory highlighting the importance of graph theory to quantum walks.As before, the reader will benefit from the pedagogical elements of the book, which include exercises and references to deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks.Review of the first edition:“The book is nicely written, the concepts are introduced naturally, and many meaningful connections between them are highlighted. The author proposes a series of exercises that help the reader get some working experience with the presented concepts, facilitating a better understanding. Each chapter ends with a discussion of further references, pointing the reader to major results on the topics presented in the respective chapter.” - Florin Manea, zbMATH.
Quantum Walks and Search Algorithms
by Renato PortugalThis book addresses an interesting area of quantum computation called quantum walks, which play an important role in building quantum algorithms, in particular search algorithms. Quantum walks are the quantum analogue of classical random walks. It is known that quantum computers have great power for searching unsorted databases. This power extends to many kinds of searches, particularly to the problem of finding a specific location in a spatial layout, which can be modeled by a graph. The goal is to find a specific node knowing that the particle uses the edges to jump from one node to the next. This book is self-contained with main topics that include: Grover's algorithm, describing its geometrical interpretation and evolution by means of the spectral decomposition of the evolution operatorAnalytical solutions of quantum walks on important graphs like line, cycles, two-dimensional lattices, and hypercubes using Fourier transformsQuantum walks on generic graphs, describing methods to calculate the limiting distribution and mixing timeSpatial search algorithms, with emphasis on the abstract search algorithm (the two-dimensional lattice is used as an example)Szedgedy's quantum-walk model and a natural definition of quantum hitting time (the complete graph is used as an example)The reader will benefit from the pedagogical aspects of the book, learning faster and with more ease than would be possible from the primary research literature. Exercises and references further deepen the reader's understanding, and guidelines for the use of computer programs to simulate the evolution of quantum walks are also provided.
Quantum Waveguides
by Pavel Exner Hynek KovaříkThis monograph explains the theory of quantum waveguides, that is, dynamics of quantum particles confined to regions in the form of tubes, layers, networks, etc. The focus is on relations between the confinement geometry on the one hand and the spectral and scattering properties of the corresponding quantum Hamiltonians on the other. Perturbations of such operators, in particular, by external fields are also considered. The volume provides a unique summary of twenty-five years of research activity in this area and indicates ways in which the theory can develop further. The book is fairly self-contained. While it requires some broader mathematical physics background, all the basic concepts are properly explained and proofs of most theorems are given in detail, so there is no need for additional sources. Without a parallel in the literature, the monograph by Exner and Kovarik guides the reader through this new and exciting field.
Quantum Wells, Wires and Dots
by Paul HarrisonQuantum Wells, Wires and Dots, 3rd Edition is aimed at providing all the essential information, both theoretical and computational, in order that the reader can, starting from essentially nothing, understand how the electronic, optical and transport properties of semiconductor heterostructures are calculated. Completely revised and updated, this text is designed to lead the reader through a series of simple theoretical and computational implementations, and slowly build from solid foundations, to a level where the reader can begin to initiate theoretical investigations or explanations of their own.