Spectral Asymptotics In The Semi Classical Limit

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Spectral Asymptotics In The Semi Classical Limit

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Author : M. Dimassi
language : en
Publisher:
Release Date : 1999

Spectral Asymptotics In The Semi Classical Limit written by M. Dimassi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Approximation theory categories.

This book presents the basic methods and applications in semiclassical approximation in the light of developments.

Spectral Asymptotics In The Semi Classical Limit

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Author : Mouez Dimassi
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-16

Spectral Asymptotics In The Semi Classical Limit written by Mouez Dimassi 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 1999-09-16 with Mathematics categories.

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.

Spectral Asymptotics In The Semi Classical Limit

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Author : Mouez Dimassi
language : en
Publisher:
Release Date : 2014-05-14

Spectral Asymptotics In The Semi Classical Limit written by Mouez Dimassi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with SCIENCE categories.

This book presents the basic methods and applications in semiclassical approximation in the light of developments.

Semiclassical Analysis

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Author : Maciej Zworski
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Semiclassical Analysis written by Maciej Zworski 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 2012 with Mathematics categories.

"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.

Semiclassical Analysis Witten Laplacians And Statistical Mechanics

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Author : Bernard Helffer
language : en
Publisher: World Scientific
Release Date : 2002

Semiclassical Analysis Witten Laplacians And Statistical Mechanics written by Bernard Helffer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. In addition, it compares the Witten Laplacian approach with other techniques, such as the transfer matrix approach and its semiclassical analysis. The author concludes by providing a complete proof of the uniform Log-Sobolev inequality.

Semiclassical Analysis

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Author : Maciej Zworski
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-09

Semiclassical Analysis written by Maciej Zworski and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-09 with Mathematics categories.

This book is an excellent, comprehensive introduction to semiclassical analysis. I believe it will become a standard reference for the subject. —Alejandro Uribe, University of Michigan Semiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel–Kramers–Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.

Topics In The Theory Of Schr Dinger Operators

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Author : Huzihiro Araki
language : en
Publisher: World Scientific
Release Date : 2004

Topics In The Theory Of Schr Dinger Operators written by Huzihiro Araki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.

This invaluable book presents reviews of some recent topics in the theory of Schr”dinger operators. It includes a short introduction to the subject, a survey of the theory of the Schr”dinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.

Semi Classical Analysis

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Author : Victor Guillemin
language : en
Publisher:
Release Date : 2013

Semi Classical Analysis written by Victor Guillemin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Fourier integral operators categories.

An Introduction To Semiclassical And Microlocal Analysis

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Author : André Bach
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

An Introduction To Semiclassical And Microlocal Analysis written by André Bach 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 2013-03-14 with Mathematics categories.

The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are mainly addressed to nonspecialists in the subject, and their purpose is to present in a pedagogical way most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard Coo pseudodifferential calculus and the analytic microlocal analysis are developed, in a context that remains intentionally global so that only the relevant difficulties of the theory are encountered. The main original ity lies in the fact that we derive all the main features of analytic microlocal analysis from a single a priori estimate, which turns out to be elementary once the Coo pseudodifferential calculus is established. Various detailed exercises are given at the end of the main chapters, most of them being easily solvable by students. Besides illustrating the main results of the lecture, their aim is also to introduce the reader to various further developments of the theory, such as the functional calculus of pseudodifferential operators, properties of the analytic wave front set, Gevrey classes, the use of coherent states, the notion of semiclassical measures, WKB constructions. Applications to the study of the Schrodinger operator are also discussed in the text, so that they may help the understanding of new notions or general results where they appear by replacing them in the context of quantum mechanics.

Complex Quantum Systems

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Author : Heinz Karl Heinrich Siedentop
language : en
Publisher: World Scientific
Release Date : 2013

Complex Quantum Systems written by Heinz Karl Heinrich Siedentop and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.

This volume is based on lectures given during the program Complex Quantum Systems held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many body methods originating from quantum information, and OCo the most complex OCo semirelativistic quantum electrodynamics.These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.