Author: André Bach
Publisher: Springer Science & Business Media
ISBN: 1475744951
Category : Mathematics
Languages : en
Pages : 193
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Book Description
This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. It is based on lectures taught by the author over several years, and includes many exercises providing outlines of useful applications of the semi-classical theory.
Author: Maciej Zworski
Publisher: American Mathematical Soc.
ISBN: 0821883208
Category : Mathematics
Languages : en
Pages : 448
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Book Description
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Author: Victor Ivrii
Publisher: Springer Science & Business Media
ISBN: 9783540627807
Category : Mathematics
Languages : en
Pages : 756
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Book Description
This long awaited book is devoted to the methods of microlocal semiclassical analysis in application to spectral asymptotics with accurate remainder estimates. The very powerful machinery of local and microlocal semiclassical spectral asymptotics is developed as well as methods in combining these asymptotics with spectral estimates. The rescaling technique should be mentioned as an easy as to use and very powerful tool. Many theorems, considered before as independent and difficult, now are just special cases of easy corollaries of the theorems proved in the book. Most of the results and almost all the proofs are as yet unpublished
Author: Alain Grigis
Publisher: Cambridge University Press
ISBN: 9780521449861
Category : Mathematics
Languages : fr
Pages : 164
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Book Description
This book corresponds to a graduate course given many times by the authors, and should prove to be useful to mathematicians and theoretical physicists.
Author: Lina Martins
Publisher:
ISBN: 9781475744965
Category :
Languages : en
Pages : 204
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Book Description
Author: Frédéric Pham
Publisher: Springer Science & Business Media
ISBN: 0857296035
Category : Mathematics
Languages : en
Pages : 218
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Book Description
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
Author: Maciej Zworski
Publisher: American Mathematical Society
ISBN: 1470470624
Category : Mathematics
Languages : en
Pages : 431
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Book Description
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.
Author: Victor Guillemin
Publisher:
ISBN: 9781571462763
Category : Fourier integral operators
Languages : en
Pages : 446
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Book Description
Author: Mouez Dimassi
Publisher: Cambridge University Press
ISBN: 0521665442
Category : Mathematics
Languages : en
Pages : 243
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Book Description
This book presents the basic methods and applications in semiclassical approximation in the light of developments.
Author: Semyon Dyatlov
Publisher: American Mathematical Soc.
ISBN: 147044366X
Category : Mathematics
Languages : en
Pages : 649
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Book Description
Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
