Emergence Of The Quantum From The Classical Mathematical Aspects Of Quantum Processes

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Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes

Author : Maurice A De Gosson
Publisher : World Scientific
ISBN 13 : 1786344165
Total Pages : 306 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes by : Maurice A De Gosson

Download or read book Emergence Of The Quantum From The Classical: Mathematical Aspects Of Quantum Processes written by Maurice A De Gosson and published by World Scientific. This book was released on 2017-11-10 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of quantum mechanics from classical world mechanics is now a well-established theme in mathematical physics. This book demonstrates that quantum mechanics can indeed be viewed as a refinement of Hamiltonian mechanics, and builds on the work of George Mackey in relation to their mathematical foundations. Additionally when looking at the differences with classical mechanics, quantum mechanics crucially depends on the value of Planck's constant h. Recent cosmological observations tend to indicate that not only the fine structure constant α but also h might have varied in both time and space since the Big Bang. We explore the mathematical and physical consequences of a variation of h; surprisingly we see that a decrease of h leads to transitions from the quantum to the classical.Emergence of the Quantum from the Classical provides help to undergraduate and graduate students of mathematics, physics and quantum theory looking to advance into research in the field.

Emergence of the Quantum from the Classical

Author : Maurice A. De Gosson
Publisher :
ISBN 13 : 9781786344151
Total Pages : 306 pages
Book Rating : 4.3/5 (441 download)

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Book Synopsis Emergence of the Quantum from the Classical by : Maurice A. De Gosson

Download or read book Emergence of the Quantum from the Classical written by Maurice A. De Gosson and published by . This book was released on 2017 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Physics of Emergence and Organization

Author : Ignazio Licata
Publisher : World Scientific
ISBN 13 : 9812779949
Total Pages : 432 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Physics of Emergence and Organization by : Ignazio Licata

Download or read book Physics of Emergence and Organization written by Ignazio Licata and published by World Scientific. This book was released on 2008 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a state-of-the-art review on the Physics of Emergence. The challenge of complexity is to focus on the description levels of the observer in context-dependent situations. Emergence is not only an heuristic approach to complexity, but it also urges us to face a much deeper question ? what do we think is fundamental in the physical world?This volume provides significant and pioneering contributions based on rigorous physical and mathematical approaches ? with particular reference to the syntax of Quantum Physics and Quantum Field Theory ? dealing with the bridge-laws and their limitations between Physics and Biology, without failing to discuss the involved epistemological features.Physics of Emergence and Organization is an interdisciplinary source of reference for students and experts whose interests cross over to complexity issues.

The Strange World of Quantum Mechanics

Author : Daniel F. Styer
Publisher : Cambridge University Press
ISBN 13 : 1316101878
Total Pages : 248 pages
Book Rating : 4.3/5 (161 download)

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Book Synopsis The Strange World of Quantum Mechanics by : Daniel F. Styer

Download or read book The Strange World of Quantum Mechanics written by Daniel F. Styer and published by Cambridge University Press. This book was released on 2000-02-24 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure.

On the Emergence Theme of Physics

Author : Robert Carroll
Publisher : World Scientific
ISBN 13 : 9814291803
Total Pages : 288 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis On the Emergence Theme of Physics by : Robert Carroll

Download or read book On the Emergence Theme of Physics written by Robert Carroll and published by World Scientific. This book was released on 2010 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

Mathematics of Classical and Quantum Physics

Author : Frederick W. Byron
Publisher : Courier Corporation
ISBN 13 : 0486135063
Total Pages : 674 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Mathematics of Classical and Quantum Physics by : Frederick W. Byron

Download or read book Mathematics of Classical and Quantum Physics written by Frederick W. Byron and published by Courier Corporation. This book was released on 2012-04-26 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians (2nd Edition)

Author : Franco Strocchi
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107367
Total Pages : 193 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians (2nd Edition) by : Franco Strocchi

Download or read book Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians (2nd Edition) written by Franco Strocchi and published by World Scientific Publishing Company. This book was released on 2008-10-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second printing contains a critical discussion of Dirac derivation of canonical quantization, which is instead deduced from general geometric structures. This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. The mathematical structure of QM is formulated in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables, for a general physical system.The Dirac-von Neumann axioms are then derived. The description of states and observables as Hilbert space vectors and operators follows from the GNS and Gelfand-Naimark Theorems. The experimental existence of complementary observables for atomic systems is shown to imply the noncommutativity of the observable algebra, the distinctive feature of QM; for finite degrees of freedom, the Weyl algebra codifies the experimental complementarity of position and momentum (Heisenberg commutation relations) and Schrödinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the Hamiltonian and solved by the Kato-Rellich conditions on the potential, which also guarantee quantum stability for classically unbounded-below Hamiltonians. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), to the formulation in terms of ground state correlations (the quantum mechanical analog of the Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle is discussed in detail, as an example of the interplay between topology and functional integral, leading to the emergence of superselection rules and θ sectors.

Picturing Quantum Processes

Author : Bob Coecke
Publisher : Cambridge University Press
ISBN 13 : 1108107710
Total Pages : 847 pages
Book Rating : 4.1/5 (81 download)

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Book Synopsis Picturing Quantum Processes by : Bob Coecke

Download or read book Picturing Quantum Processes written by Bob Coecke and published by Cambridge University Press. This book was released on 2017-03-16 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.

Quantum Foundations, Probability and Information

Author : Andrei Khrennikov
Publisher : Springer
ISBN 13 : 3319749714
Total Pages : 304 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Quantum Foundations, Probability and Information by : Andrei Khrennikov

Download or read book Quantum Foundations, Probability and Information written by Andrei Khrennikov and published by Springer. This book was released on 2018-06-13 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory. Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.

Mathematical Horizons for Quantum Physics

Author : Huzihiro Araki
Publisher : World Scientific
ISBN 13 : 9814313327
Total Pages : 221 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Mathematical Horizons for Quantum Physics by : Huzihiro Araki

Download or read book Mathematical Horizons for Quantum Physics written by Huzihiro Araki and published by World Scientific. This book was released on 2010 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control of the molecular alignment or orientation by laser pulses / Arne Keller -- Quantum computing and devices : A short introduction / Zhigang Zhang, Viswanath Ramakrishna and Goong Chen -- Dynamics of mixed classical-quantum systems, geometric quantization and coherent states / Hans-Rudolf Jauslin and Dominique Sugny -- Quantum memories as open systems / Robert Alicki -- Two mathematical problems in quantum information theory / Alexander S. Holevo -- Dissipatively induced bipartite entanglement / Fabio Benatti -- Scattering in nonrelativistic quantum field theory / Jan Derezinski -- Mathematical theory of atoms and molecules / Volker Bach

Markov Processes and Quantum Theory

Author : Masao Nagasawa
Publisher : Springer Nature
ISBN 13 : 3030626881
Total Pages : 339 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Markov Processes and Quantum Theory by : Masao Nagasawa

Download or read book Markov Processes and Quantum Theory written by Masao Nagasawa and published by Springer Nature. This book was released on 2021-06-23 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schrödinger equation is a complex-valued evolution equation and the Schrödinger function is a complex-valued evolution function, important applications are given. Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.

Quantum-Classical Analogies

Author : Daniela Dragoman
Publisher : Springer Science & Business Media
ISBN 13 : 3662096471
Total Pages : 355 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quantum-Classical Analogies by : Daniela Dragoman

Download or read book Quantum-Classical Analogies written by Daniela Dragoman and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.

Mathematical Aspects of Quantum Computing 2007

Author : Mikio Nakahara
Publisher : World Scientific
ISBN 13 : 9812814477
Total Pages : 239 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Mathematical Aspects of Quantum Computing 2007 by : Mikio Nakahara

Download or read book Mathematical Aspects of Quantum Computing 2007 written by Mikio Nakahara and published by World Scientific. This book was released on 2008 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of the mathematical aspects of quantum computing. It will be useful for graduate students and researchers interested in quantum computing from different areas of physics, mathematics, informatics and computer science. The lecture notes in this volume are written in a self-contained style, and hence are accessible for graduate students and researchers with even less background in the topics.

Path Integrals and Quantum Processes

Author : Mark S. Swanson
Publisher : Courier Corporation
ISBN 13 : 0486782301
Total Pages : 463 pages
Book Rating : 4.4/5 (867 download)

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Book Synopsis Path Integrals and Quantum Processes by : Mark S. Swanson

Download or read book Path Integrals and Quantum Processes written by Mark S. Swanson and published by Courier Corporation. This book was released on 2014-02-19 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.

The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson

Author : Arkady Plotnitsky
Publisher : Springer
ISBN 13 : 3319320688
Total Pages : 341 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson by : Arkady Plotnitsky

Download or read book The Principles of Quantum Theory, From Planck's Quanta to the Higgs Boson written by Arkady Plotnitsky and published by Springer. This book was released on 2016-09-26 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book considers foundational thinking in quantum theory, focusing on the role the fundamental principles and principle thinking there, including thinking that leads to the invention of new principles, which is, the book contends, one of the ultimate achievements of theoretical thinking in physics and beyond. The focus on principles, prominent during the rise and in the immediate aftermath of quantum theory, has been uncommon in more recent discussions and debates concerning it. The book argues, however, that exploring the fundamental principles and principle thinking is exceptionally helpful in addressing the key issues at stake in quantum foundations and the seemingly interminable debates concerning them. Principle thinking led to major breakthroughs throughout the history of quantum theory, beginning with the old quantum theory and quantum mechanics, the first definitive quantum theory, which it remains within its proper (nonrelativistic) scope. It has, the book also argues, been equally important in quantum field theory, which has been the frontier of quantum theory for quite a while now, and more recently, in quantum information theory, where principle thinking was given new prominence. The approach allows the book to develop a new understanding of both the history and philosophy of quantum theory, from Planck’s quantum to the Higgs boson, and beyond, and of the thinking the key founding figures, such as Einstein, Bohr, Heisenberg, Schrödinger, and Dirac, as well as some among more recent theorists. The book also extensively considers the nature of quantum probability, and contains a new interpretation of quantum mechanics, “the statistical Copenhagen interpretation.” Overall, the book’s argument is guided by what Heisenberg called “the spirit of Copenhagen,” which is defined by three great divorces from the preceding foundational thinking in physics—reality from realism, probability from causality, and locality from relativity—and defined the fundamental principles of quantum theory accordingly.

Quantum Harmonic Analysis

Author : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110722771
Total Pages : 240 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Quantum Harmonic Analysis by : Maurice A. de Gosson

Download or read book Quantum Harmonic Analysis written by Maurice A. de Gosson and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

The Quantum Vacuum

Author : Peter W. Milonni
Publisher : Academic Press
ISBN 13 : 0080571492
Total Pages : 539 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis The Quantum Vacuum by : Peter W. Milonni

Download or read book The Quantum Vacuum written by Peter W. Milonni and published by Academic Press. This book was released on 2013-10-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: In modern physics, the classical vacuum of tranquil nothingness has been replaced by a quantum vacuum with fluctuations of measurable consequence. In The Quantum Vacuum, Peter Milonni describes the concept of the vacuum in quantum physics with an emphasis on quantum electrodynamics. He elucidates in depth and detail the role of the vacuum electromagnetic field in spontaneous emission, the Lamb shift, van der Waals, and Casimir forces, and a variety of other phenomena, some of which are of technological as well as purely scientific importance. This informative text also provides an introduction based on fundamental vacuum processes to the ideas of relativistic quantum electrodynamics and quantum field theory, including renormalization and Feynman diagrams. Experimental as well as theoreticalaspects of the quantum vacuum are described, and in most cases details of mathematical derivations are included. Chapter 1 of The Quantum Vacuum - published in advance in The American Journal of Physics (1991)-was later selected by readers as one of the Most Memorable papers ever published in the 60-year history of the journal. This chapter provides anexcellent beginning of the book, introducing a wealth of information of historical interest, the results of which are carefully woven into subsequent chapters to form a coherent whole. Does not assume that the reader has taken advanced graduate courses, making the text accessible to beginning graduate students Emphasizes the basic physical ideas rather than the formal, mathematical aspects of the subject Provides a careful and thorough treatment of Casimir and van der Waals forces at a level of detail not found in any other book on this topic Clearly presents mathematical derivations