Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians
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Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians
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Author : Matteo Gallone
language : en
Publisher: Springer Nature
Release Date : 2023-04-04
Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians written by Matteo Gallone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-04 with Science categories.
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience). Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels, unitary evolution and, more generally, a self-consistent theory. Physical heuristics often produce candidate Hamiltonians that are only symmetric: their extension to suitably larger domains of self-adjointness, when possible, amounts to declaring additional physical states the operator must act on in order to have a consistent physics, and distinct self-adjoint extensions describe different physics. Realising observables self-adjointly is the first fundamental problem of quantum-mechanical modelling. The discussed applications concern models of topical relevance in modern mathematical physics currently receiving new or renewed interest, in particular from the point of view of classifying self-adjoint realisations of certain Hamiltonians and studying their spectral and scattering properties. The analysis also addresses intermediate technical questions such as characterising the corresponding operator closures and adjoints. Applications include hydrogenoid Hamiltonians, Dirac–Coulomb Hamiltonians, models of geometric quantum confinement and transmission on degenerate Riemannian manifolds of Grushin type, and models of few-body quantum particles with zero-range interaction. Graduate students and non-expert readers will benefit from a preliminary mathematical chapter collecting all the necessary pre-requisites on symmetric and self-adjoint operators on Hilbert space (including the spectral theorem), and from a further appendix presenting the emergence from physical principles of the requirement of self-adjointness for observables in quantum mechanics.
Mathematics Going Forward
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Author : Jean-Michel Morel
language : en
Publisher: Springer Nature
Release Date : 2023-05-13
Mathematics Going Forward written by Jean-Michel Morel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-13 with Mathematics categories.
This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.
Mathematical Challenges Of Zero Range Physics
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Author : Alessandro Michelangeli
language : en
Publisher: Springer Nature
Release Date : 2021-02-04
Mathematical Challenges Of Zero Range Physics written by Alessandro Michelangeli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-04 with Science categories.
Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
From Micro To Macro Quantum Systems A Unified Formalism With Superselection Rules And Its Applications
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Author : K Kong Wan
language : en
Publisher: World Scientific
Release Date : 2006-03-03
From Micro To Macro Quantum Systems A Unified Formalism With Superselection Rules And Its Applications written by K Kong Wan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-03 with Science categories.
Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations.This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schrödinger's cat states in superconducting systems, and a path space formulation of quantum mechanics.This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators./a
Mathematical Challenges Of Zero Range Physics
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Author : Alessandro Michelangeli
language : en
Publisher:
Release Date : 2021
Mathematical Challenges Of Zero Range Physics written by Alessandro Michelangeli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
Classical And Quantum Physics
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Author : G. Marmo
language : en
Publisher: Springer Nature
Release Date : 2019-10-26
Classical And Quantum Physics written by G. Marmo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-26 with Science categories.
This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.
The Quantum Self
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Author : Danah Zohar
language : en
Publisher:
Release Date : 1991
The Quantum Self written by Danah Zohar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mind and body categories.
In The Quantum Self, Danah Zohar argues that the insights of modem physics can illuminate our understanding of everyday life -- our relationships to ourselves, to others, and to the world at large. Guiding us through the strange and fascinating workings of the subatomic realm to create a new model of human consciousness, the author addresses enduring philosophical questions. Does the new physics provide a basis by which our consciousness might continue beyond death? How does the material world (for instance, ugly inner cities) impinge upon our sense of self? Is there a subatomic wellspring from which our creativity, our empathy with others, and our feelings of unity with the inanimate world originate?Most important, Zohar shows how the vitality of the new physics combats the alienation and fragmentation of twentieth-century life, and replaces it with a model of reality in which the universe itself may possess a type of consciousness, of which human consciousness is one expression.
American Doctoral Dissertations
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Author :
language : en
Publisher:
Release Date : 1968
American Doctoral Dissertations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Dissertation abstracts categories.
The Cellular Automaton Interpretation Of Quantum Mechanics
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Author : Gerard 't Hooft
language : en
Publisher: Springer
Release Date : 2016-09-02
The Cellular Automaton Interpretation Of Quantum Mechanics written by Gerard 't Hooft and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-02 with Science categories.
This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The author gives examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of the wave function collapse and the measurement problem. Even the existence of an “arrow of time" can perhaps be explained in a more elegant way than usual. As well as reviewing the author’s earlier work in the field, the book also contains many new observations and calculations. It provides stimulating reading for all physicists working on the foundations of quantum theory.
Ubiquitous Quantum Structure
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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-23
Ubiquitous Quantum Structure written by Andrei Y. Khrennikov 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 2010-01-23 with Science categories.
Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.