The Classical Quantum Correspondence
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The Classical Quantum Correspondence
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Author : Benjamin H. Feintzeig
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-31
The Classical Quantum Correspondence written by Benjamin H. Feintzeig and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-31 with Science categories.
This Element provides an entry point for philosophical engagement with quantization and the classical limit. It introduces the mathematical tools of C*-algebras as they are used to compare classical and quantum physics. It then employs those tools to investigate philosophical issues surrounding theory change in physics. It discusses examples in which quantization bears on the topics of reduction, structural continuity, analogical reasoning, and theory construction. In doing so, it demonstrates that the precise mathematical tools of algebraic quantum theory can aid philosophers of science and philosophers of physics.
Quantum Classical Correspondence
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Author : A. O. Bolivar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Quantum Classical Correspondence written by A. O. Bolivar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.
At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.
From C Numbers To Q Numbers
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Author : Olivier Darrigol
language : en
Publisher: University of California Press
Release Date : 2021-01-08
From C Numbers To Q Numbers written by Olivier Darrigol and has been published by University of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-08 with Science categories.
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992.
The Classical Quantum Correspondence Of Polyatomic Molecules
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Author : Suzanne Michelle Pittman
language : en
Publisher:
Release Date : 2016
The Classical Quantum Correspondence Of Polyatomic Molecules written by Suzanne Michelle Pittman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
As a result of the ubiquitous numerical errors that accumulate during numerical studies of Arnol'd Diffusion, we use a physically motivated non-convex Hamiltonian that features fast diffusion along the Arnol'd web. Fast diffusion is a worst case scenario as a competitor to dynamical tunneling. We show how dynamical tunneling dominates fast diffusion, suggesting that dynamical tunneling is the prime culprit of the narrow peak splittings in high-resolution IR spectra of polyatomic molecules.
Classical Quantum Correspondence And Periodic Orbits In Doubly Excited States Of The Helium Atom
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Author : Jong-Hyun Kim
language : en
Publisher:
Release Date : 1993
Classical Quantum Correspondence And Periodic Orbits In Doubly Excited States Of The Helium Atom written by Jong-Hyun Kim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Quantum Classical Correspondence For The Fourier Spectrum Of A Trajectory
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Author :
language : en
Publisher:
Release Date : 1982
Quantum Classical Correspondence For The Fourier Spectrum Of A Trajectory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
The question of classical-quantum correspondence of the Fourier spectrum of a classical variable is addressed. (GHT).
Practicing The Correspondence Principle In The Old Quantum Theory
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Author : Martin Jähnert
language : en
Publisher: Springer
Release Date : 2019-06-20
Practicing The Correspondence Principle In The Old Quantum Theory written by Martin Jähnert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with Science categories.
This book presents a history of the correspondence principle from a new perspective. The author provides a unique exploration of the relation between the practice of theory and conceptual development in physics. In the process, he argues for a new understanding of the history of the old quantum theory and the emergence of quantum mechanics. The analysis looks at how the correspondence principle was disseminated and how the principle was applied as a research tool during the 1920s. It provides new insights into the interaction between theoretical tools and scientific problems and shows that the use of this theoretical tool changed the tool itself in a process of transformation through implementation. This process, the author claims, was responsible for the conceptual development of the correspondence principle. This monograph connects to the vast literature in the history of science, which analyzed theoretical practices as based on tacit knowledge, skills, and calculation techniques. It contributes to the historical understanding of quantum physics and the emergence of quantum mechanics. Studying how physicists used a set of tools to solve problems, the author spells out the ‟skillful guessing” that went into the making of quantum theoretical arguments and argues that the integration and implementation of technical resources was a central driving force for the conceptual and theoretical transformation in the old quantum theory.
The Correspondence Principle 1918 1923
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Author : J.R. Nielsen
language : en
Publisher: Elsevier
Release Date : 2013-10-22
The Correspondence Principle 1918 1923 written by J.R. Nielsen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
During this period Bohr's researches had a double aim: to develop a consistent and adequate quantum theory and to explain the structures and properties of the elements of the periodic system. ``The Correspondence Principle'' contains the papers and manuscripts dealing mainly with the elaboration of the general quantum theory.
The Foundations Of Quantum Theory
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Author : Sol Wieder
language : en
Publisher: Elsevier
Release Date : 2012-12-02
The Foundations Of Quantum Theory written by Sol Wieder and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
The Foundations of Quantum Theory discusses the correspondence between the classical and quantum theories through the Poisson bracket-commutator analogy. The book is organized into three parts encompassing 12 chapters that cover topics on one-and many-particle systems and relativistic quantum mechanics and field theory. The first part of the book discusses the developments that formed the basis for the old quantum theory and the use of classical mechanics to develop the theory of quantum mechanics. This part includes considerable chapters on the formal theory of quantum mechanics and the wave mechanics in one- and three-dimension, with an emphasis on Coulomb problem or the hydrogen atom. The second part deals with the interacting particles and noninteracting indistinguishable particles and the material covered is fundamental to almost all branches of physics. The third part presents the pertinent equations used to illustrate the relativistic quantum mechanics and quantum field theory. This book is of value to undergraduate physics students and to students who have background in mechanics, electricity and magnetism, and modern physics.
Quantum Classical Correspondence And Entanglement In Periodically Driven Spin Systems
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Author : Meenu Kumari
language : en
Publisher:
Release Date : 2019
Quantum Classical Correspondence And Entanglement In Periodically Driven Spin Systems written by Meenu Kumari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This dissertation sets out to examine some fundamental open questions in quantum physics regarding quantum-classical correspondence in regular versus chaotic systems. Specifically, we study these questions using approaches in quantum information science in an experimentally realized textbook model of quantum chaos - the quantum kicked top (QKT). The effect of classical chaos on the generation of entanglement in spin systems has been a field of active research for a couple of decades. Whether high entanglement in these systems is a hallmark of chaos or not remains a widely debated topic. We explain the connection between entanglement and chaos in spin systems and resolve previous conflicting results. The previous studies have mostly drawn conclusions from numerical work on a few initial states in regular versus chaotic regions. We instead focus on stable and unstable periodic orbits because chaos emerges around unstable periodic orbits. We first propose a new set of criteria for determining whether quantum evolution will correspond to the classical trajectory in a localized manner at stable periodic orbits in periodically driven systems. These criteria can be used to calculate the quantum numbers that will lead to quantum-classical correspondence even in a deep quantum regime, and thus to quantify the well-known Bohr correspondence principle. Next, we analytically show a direct connection between entanglement generation and a measure of delocalization of a quantum state in spin systems. More concretely, we describe a method to calculate an upper bound on entanglement generation in any bipartition of spin systems, where the upper bound is a function of trace distance between the evolved state and the most localized classical-like separable states. This method along with our criteria for localized evolution enables us to explain the behaviour of entanglement in both deep quantum and semiclassical regimes for regular as well as chaotic regions. Hence, our analysis resolves the long-standing debates regarding the connection between classical chaos and quantum entanglement in deep quantum and semiclassical regimes. In addition to the study of entanglement, we perform the first study of nonlocality, and the effect of chaos on its generation in the QKT. Since nonlocality and entanglement are inequivalent quantum resources, the effect of chaos on nonlocality merits an explicit study. Violations of Bell inequalities in the presence of spacelike separation among the subsystems imply nonlocality - meaning nonlocal correlations between subsystems of the total spin system. We show that the QKT evolution can lead to states that violate multiqubit Bell inequalities and hence provides a deterministic method to prepare nonlocal quantum states. Our numerical results suggest a correlation between delocalized evolution of a pure quantum state and generation of nonlocality in the quantum state. We further demonstrate that dynamical tunnelling - a classically forbidden phenomenon - in the QKT leads to the generation of Greenberger-Horne-Zeilinger (GHZ)-like states for even numbers of qubits. We analytically prove that these states are maximally nonlocal. On the other hand, we numerically show that any reduced state of the QKT obtained by tracing out a subsystem of the total spin system does not violate Bell inequalities. We provide an analytical explanation of the numerical results for $2-$qubit reduced states by formulating and proving two general theorems regarding $2-$qubit Bell inequalities. These theorems imply that any $2-$qubit mixed state having a symmetric extension or symmetric purification cannot violate the Clauser-Horne-Shimony-Holt inequality. This highlights fundamental connections between two important and distinct concepts in quantum information science - Bell inequalities and symmetric extension of quantum states. Apart from providing deeper insights into the fundamental questions of quantum-classical correspondence and new approaches to analyze quantum chaos, the methods developed in this thesis can be used to design quantum systems that can efficiently generate entanglement and nonlocality. Thus, our results could have interesting applications in quantum computing and quantum information science.