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

Author : De Gosson Maurice A
Publisher : World Scientific
Page : 308 pages
File Size : 52,9 Mb
Release : 2017-11-10
Category : Science
ISBN : 9781786344168

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

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. Contents: Hamiltonian MechanicsHamilton–Jacobi TheoryMatter Waves, Schrödinger's Equation, and Bohm's Theory The MetatronUncertainties and Quantum BlobsQuantum States and the Density MatrixVarying Planck's ConstantAppendices: The Symplectic GroupThe Metaplectic RepresentationBorn–Jordan QuantizationTwisted Product and Convolution Readership: Undergraduate and graduate students of mathematics and physics, interested in analysis and differential equations, probability and statistics, geometry and topology and mathematical physics. Keywords: Classical Mechanics;Hamiltonian Mechanics;Quantum Mechanics;Planck's Constant;Mathematical Physics;Algebraic GeometryReview:0

Author : Maurice A. De Gosson
Publisher : Unknown
Page : 306 pages
File Size : 47,7 Mb
Release : 2017
Category : SCIENCE
ISBN : 1786344157

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Emergence of the Quantum from the Classical by Maurice A. De Gosson Pdf

Author : Ruth E Kastner,Jasmina Jeknić-Dugić,George Jaroszkiewicz
Publisher : World Scientific
Page : 500 pages
File Size : 55,9 Mb
Release : 2016-11-10
Category : Science
ISBN : 9781786341426

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Quantum Structural Studies by Ruth E Kastner,Jasmina Jeknić-Dugić,George Jaroszkiewicz Pdf

The structural aspects of composite quantum systems in the foundation, interpretation and application of quantum theory is an increasingly prominent topic of physics research. As an emerging field, it seeks to understand the origins of the classical world of experience from the quantum level. Quantum Structural Studies presents conceptual fundamentals and mathematical methods for investigating the structuring of quantum systems into subsystems. Split into four sections, the topics covered include the historical and philosophical aspects of quantum structures, specific interpretive approaches and ontologies, and alternative methodological approaches to quantum mechanics. Questions addressed are: Can the classically relevant degrees of freedom (such as the center of mass) be considered physically realistic, and if so, in what sense?In what sense might various emergent structures be relevant for the transition from the quantum description to the classical?Do suggested new approaches describe phenomenology and proposals for new experiments? Specialists, graduate students and researchers seeking an introduction to the field of emergent structures and new directions for research and experimentation can use this book to find up-to-date representative texts and reviews.

Author : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 247 pages
File Size : 40,9 Mb
Release : 2021-07-05
Category : Mathematics
ISBN : 9783110722901

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Quantum Harmonic Analysis by Maurice A. de Gosson Pdf

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.

Author : Ignazio Licata
Publisher : World Scientific
Page : 432 pages
File Size : 46,9 Mb
Release : 2008
Category : Science
ISBN : 9789812779946

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Physics of Emergence and Organization by Ignazio Licata Pdf

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.

Author : Fabio Bagarello,Jean-Pierre Gazeau,Franciszek Hugon Szafraniec,Miloslav Znojil
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 41,7 Mb
Release : 2015-07-24
Category : Science
ISBN : 9781118855263

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Non-Selfadjoint Operators in Quantum Physics by Fabio Bagarello,Jean-Pierre Gazeau,Franciszek Hugon Szafraniec,Miloslav Znojil Pdf

A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

Author : Robert Carroll
Publisher : World Scientific
Page : 288 pages
File Size : 40,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814291804

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On the Emergence Theme of Physics by Robert Carroll Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,7 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814471077

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Mathematical Aspects of Quantum Computing 2007 by Anonim Pdf

Author : Mikio Nakahara,Robabeh Rahimi,Akira SaiToh
Publisher : World Scientific
Page : 239 pages
File Size : 48,6 Mb
Release : 2008
Category : Science
ISBN : 9789812814470

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Mathematical Aspects of Quantum Computing 2007 by Mikio Nakahara,Robabeh Rahimi,Akira SaiToh Pdf

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.

Author : Jasmina Jeknić-Dugić,Ruth E. Kastner,George Jaroszkiewicz
Publisher : Unknown
Page : 128 pages
File Size : 47,6 Mb
Release : 2016
Category : Atomic structure
ISBN : 1786341417

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Quantum Structural Studies by Jasmina Jeknić-Dugić,Ruth E. Kastner,George Jaroszkiewicz Pdf

"The structural aspects of composite quantum systems in the foundation, interpretation and application of quantum theory is an increasingly prominent topic of physics research. As an emerging field, it seeks to understand the origins of the classical world of experience from the quantum level. Quantum Structural Studies presents conceptual fundamentals and mathematical methods for investigating the structuring of quantum systems into subsystems. Split into four sections, the topics covered include the historical and philosophical aspects of quantum structures, specific interpretive approaches and ontologies, and alternative methodological approaches to quantum mechanics. Questions addressed are: Can the classically relevant degrees of freedom (such as the center of mass) be considered physically realistic, and if so, in what sense? In what sense might various emergent structures be relevant for the transition from the quantum description to the classical? Do suggested new approaches describe phenomenology and proposals for new experiments? Specialists, graduate students and researchers seeking an introduction to the field of emergent structures and new directions for research and experimentation can use this book to find up-to-date representative texts and reviews."--Publisher's website

Author : Mikio Nakahara,Robabeh Rahimi,Akira SaiToh
Publisher : World Scientific
Page : 239 pages
File Size : 44,6 Mb
Release : 2008
Category : Computers
ISBN : 9789812814487

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Mathematical Aspects of Quantum Computing 2007 by Mikio Nakahara,Robabeh Rahimi,Akira SaiToh Pdf

Quantum computing: an overview / M. Nakahara -- Braid group and topological quantum computing / T. Ootsuka, K. Sakuma -- An introduction to entanglement theory / D.J.H. Markham -- Holonomic quantum computing and its optimization / S. Tanimura -- Playing games in quantum mechanical settings: features of quantum games / S̮. K. Özdemir, J. Shimamura, N. Imoto -- Quantum error-correcting codes / M. Hagiwara -- Poster summaries. Controled teleportation of an arbitrary unknown two-qubit entangled state / V. Ebrahimi, R. Rahimi, M. Nakahara. Notes on the Dür-Cirac classification / Y. Ota, M. Yoshida, I. Ohba. Bang-bang control of entanglement in Spin-Bus-Boson model / R. Rahimi, A. SaiToh, M. Nakahara. Numerical computation of time-dependent multipartite nonclassical correlation / A. SaiToh [und weitere]. On classical no-cloning theorem under Liouville dynamics and distances / T. Yamano, O. Iguchi

Author : John Watrous
Publisher : Unknown
Page : 599 pages
File Size : 47,8 Mb
Release : 2018-04-26
Category : Computers
ISBN : 9781107180567

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The Theory of Quantum Information by John Watrous Pdf

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

Author : Masao Nagasawa
Publisher : Springer Nature
Page : 339 pages
File Size : 46,8 Mb
Release : 2021-06-23
Category : Computers
ISBN : 9783030626884

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Markov Processes and Quantum Theory by Masao Nagasawa Pdf

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.

Author : Rajendra K. Bera
Publisher : Springer Nature
Page : 278 pages
File Size : 41,8 Mb
Release : 2020-03-14
Category : Science
ISBN : 9789811524714

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The Amazing World of Quantum Computing by Rajendra K. Bera Pdf

This book discusses the application of quantum mechanics to computing. It explains the fundamental concepts of quantum mechanics and then goes on to discuss various elements of mathematics required for quantum computing. Quantum cryptography, waves and Fourier analysis, measuring quantum systems, comparison to classical mechanics, quantum gates, and important algorithms in quantum computing are among the topics covered. The book offers a valuable resource for graduate and senior undergraduate students in STEM (science, technology, engineering, and mathematics) fields with an interest in designing quantum algorithms. Readers are expected to have a firm grasp of linear algebra and some familiarity with Fourier analysis.

Author : Jagdish Mehra,Helmut Rechenberg
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 51,5 Mb
Release : 2000-12-28
Category : Science
ISBN : 0387951784

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The Historical Development of Quantum Theory by Jagdish Mehra,Helmut Rechenberg Pdf

Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.