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Spectral Analysis Of Quantum Hamiltonians


Spectral Analysis Of Quantum Hamiltonians
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Spectral Analysis Of Quantum Hamiltonians


Spectral Analysis Of Quantum Hamiltonians
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Author : Rafael Benguria
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-30

Spectral Analysis Of Quantum Hamiltonians written by Rafael Benguria 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 2012-06-30 with Mathematics categories.


This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.​



Spectral Analysis Of An Effective Hamiltonian In Nonrelativistic Quantum Electrodynamics


Spectral Analysis Of An Effective Hamiltonian In Nonrelativistic Quantum Electrodynamics
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Author : Asao Arai
language : en
Publisher:
Release Date : 2010

Spectral Analysis Of An Effective Hamiltonian In Nonrelativistic Quantum Electrodynamics written by Asao Arai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.




Many Particle Hamiltonians


Many Particle Hamiltonians
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Author : Robert Adolʹfovich Minlos
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Many Particle Hamiltonians written by Robert Adolʹfovich Minlos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Hamiltonian systems categories.


This collection deals with several different topics related to the construction and spectral analysis of Hamiltonians of various systems arising in mathematical physics. Included are a study of the disposition and character of resonances for certain operators, with applications to solid body physics; a survey of work in the perturbation of Hamiltonians in fermion systems; an examination of the construction of the Hamiltonian for three different pointwise interacting quantum particles; and a study of the lower branches of the Hamiltonian of the lattice model for chromodynamics. The final paper presents an extensive survey of problems related to the spectrum of finite-particle lattice Hamiltonians, which arise in quantum field theory and in models in the theory of solid bodies. The book provides an introduction of sorts to a series of new methods and problems in mathematical physics.



Spectral Theory And Mathematical Physics


Spectral Theory And Mathematical Physics
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Author : Pablo Miranda
language : en
Publisher: Springer Nature
Release Date : 2020-11-12

Spectral Theory And Mathematical Physics written by Pablo Miranda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-12 with Mathematics categories.


This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.



Self Adjoint Extension Schemes And Modern Applications To Quantum Hamiltonians


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.



Open Quantum Systems I


Open Quantum Systems I
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Author : Stéphane Attal
language : en
Publisher: Springer
Release Date : 2006-08-18

Open Quantum Systems I written by Stéphane Attal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-18 with Mathematics categories.


Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.



Mathematical Quantum Theory Ii Schrodinger Operators


Mathematical Quantum Theory Ii Schrodinger Operators
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Author : Joel S. Feldman
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Mathematical Quantum Theory Ii Schrodinger Operators written by Joel S. Feldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.


The articles in this collection constitute the proceedings of the Canadian Mathematical Society Annual Seminar on Mathematical Quantum Theory, held in Vancouver in August 1993. The meeting was run as a research-level summer school concentrating on two related areas of contemporary mathematical physics. The first area, quantum field theory and many-body theory, is covered in volume 1 of these proceedings. The second area, treated in the present volume, is Schrödinger operators. The meeting featured a series of four-hour mini-courses, designed to introduce students to the state of the art in particular areas, and thirty hour-long expository lectures. With contributions from some of the top experts in the field, this book is an important resource for those interested in activity at the frontiers of mathematical quantum theory.



Spectral Asymptotics Of Quantum Hamiltonians


Spectral Asymptotics Of Quantum Hamiltonians
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Author : Sergey Morozov
language : en
Publisher:
Release Date : 2018

Spectral Asymptotics Of Quantum Hamiltonians written by Sergey Morozov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.




Symplectic Methods In Harmonic Analysis And In Mathematical Physics


Symplectic Methods In Harmonic Analysis And In Mathematical Physics
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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-30

Symplectic Methods In Harmonic Analysis And In Mathematical Physics written by Maurice A. de Gosson 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 2011-07-30 with Mathematics categories.


The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.



Spectral And Dynamical Properties Of Certain Quantum Hamiltonians In Dimension Two


Spectral And Dynamical Properties Of Certain Quantum Hamiltonians In Dimension Two
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Author : Josef Mehringer
language : en
Publisher:
Release Date : 2015

Spectral And Dynamical Properties Of Certain Quantum Hamiltonians In Dimension Two written by Josef Mehringer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.