Quantum Classical Correspondence

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Quantum Classical Correspondence

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Author : A. O. Bolivar
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-01-22

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 2004-01-22 with Language Arts & Disciplines 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.

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.

Quantum Classical Correspondence In Chaotic Systems

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Author : Joshua John Arthur Wilkie
language : en
Publisher:
Release Date : 1994

Quantum Classical Correspondence In Chaotic Systems written by Joshua John Arthur Wilkie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 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).

Quantum Classical Correspondence In Two Simple Systems Microform

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Author : Bradley Clarke Hughes
language : en
Publisher: National Library of Canada = Bibliothèque nationale du Canada
Release Date : 1995

Quantum Classical Correspondence In Two Simple Systems Microform written by Bradley Clarke Hughes and has been published by National Library of Canada = Bibliothèque nationale du Canada this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Chaotic behavior in systems categories.

A New Quantum

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Author : Courtlandt Bohn
language : en
Publisher:
Release Date : 1975

A New Quantum written by Courtlandt Bohn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Quantum theory categories.

Quantum Classical Correspondence In Nonrelativistic Electrodynamics

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Author :
language : en
Publisher:
Release Date : 1999

Quantum Classical Correspondence In Nonrelativistic Electrodynamics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

A form of classical electrodynamic field exists which gives exact agreement with the operator field of quantum electrodynamics (QED) for the Lamb shift of a harmonically bound point electron. Here it is pointed out that this form of classical theory with its physically acceptable interpretation is the result of an unconventional resolution of a mathematically ambiguous term in classical field theory. Finally a quantum-classical correspondence principle is shown to exist in the sense that the classical field and expectation value of the QED operator field are identical if retardation is neglected in the latter.

Progress Of Theoretical Physics

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Author :
language : en
Publisher:
Release Date : 1989

Progress Of Theoretical Physics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Physics categories.

Quantum Classical Correspondence In Nonrelativistic Electrodynamics

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Author : Burke Ritchie
language : en
Publisher:
Release Date : 1999

Quantum Classical Correspondence In Nonrelativistic Electrodynamics written by Burke Ritchie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Quantum Classical Correspondence And The Extended Jaynes Cummings Model

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Author : Timothy Charles Burt
language : en
Publisher:
Release Date : 1999

Quantum Classical Correspondence And The Extended Jaynes Cummings Model written by Timothy Charles Burt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Coupled mode theory categories.