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Saturday, August 8, 2020 | History

3 edition of KAM theory and semiclassical approximations to eigenfunctions found in the catalog.

KAM theory and semiclassical approximations to eigenfunctions

V. F. Lazutkin

KAM theory and semiclassical approximations to eigenfunctions

by V. F. Lazutkin

  • 184 Want to read
  • 22 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Hamiltonian systems.,
  • Eigenfunctions.,
  • Asymptotic distribution (Probability theory),
  • Schrödinger operator.

  • Edition Notes

    Includes bibliographical references (p. [375]-380) and index.

    StatementVladimir F. Lazutkin ; with addendum by A.I. Shnirelman.
    SeriesErgebnisse der Mathematik und ihrer Grenzgebiete ;, 3. Folge, Bd. 24
    Classifications
    LC ClassificationsQA614.83 .L39 1993
    The Physical Object
    Paginationix, 387 p. :
    Number of Pages387
    ID Numbers
    Open LibraryOL1408896M
    ISBN 100387533893, 3540533893
    LC Control Number93017491

    We study semiclassical approximations to the time evolution of coherent states for general spin-orbit coupling problems in two different semiclassical . Abstract. We show $\Bbb C^\infty$ local rigidity for $\mathbb{Z}^k$ $(k\ge 2)$ higher rank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold-Moser) iterative scheme.

      An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to being completely integrable is obtained. We apply these results to characterize the sets of semiclassical measures and . The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian over the total wave function. The .

      Vladimir F. Lazutkin, KAM theory and semiclassical approximations to eigenfunctions, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 24, Springer-Verlag, Berlin, .   that is, is the Schrödinger operator with potential. In this paper we discuss properties of the Hamiltonian operator corresponding to properties of the system described by the KAM (Kolmogorov–Arnold–Moser) theory and related theories, namely, by KAM theory proper, averaging, Nekhoroshev stability, and diffusion (this list is by no means canonical but reflects .


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KAM theory and semiclassical approximations to eigenfunctions by V. F. Lazutkin Download PDF EPUB FB2

The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory. The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schrödinger operator.

KAM Theory and Semiclassical Approximations to Eigenfunctions (Ergebnisse der Mathematik und ihrer Grenzgebiete. Folge / A Series of Modern Surveys in Mathematics) Hardcover – Aug by Vladimir F. Lazutkin Author: Vladimir F. Lazutkin. The main results concern the existence and persistence of KAM theory, their smooth dependence on the frequency, and the estimate of the measure of the set filled by KAM theory.

The second part is devoted to the construction of the semiclassical asymptotics to the eigenfunctions of the generalized Schrödinger by: KAM Theory and Semiclassical Approximations to Eigenfunctions (Ergebnisse der Mathematik und ihrer Grenzgebiete.

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KAM Theory and Semiclassical Approximations to Eigenfunctions (Ergebnisse der Mathematik und ihrer Grenzgebiete. Folge / A Series of Modern Surveys in Mathematics) by Vladimir F. Lazutkin (): Vladimir F.

Lazutkin: Books - or: Vladimir F. Lazutkin. Shnirelman A.I. () Addendum On the Asymptotic Properties of Eigenfunctions in the Regions of Chaotic Motion.

In: KAM Theory and Semiclassical Approximations to Eigenfunctions. Ergebnisse der Mathematik und ihrer Grenzgebiete (3. Folge A Series of Modern Surveys in Mathematics), vol Springer, Berlin, Heidelberg. KAM Theory and Semiclassical Approximations to Eigenfunctions Ergebnisse der Mathematik und ihrer Grenzgebiete.

Folge / A Series of Modern Surveys in Mathematics: : Vladimir F. Lazutkin, A.I. Shnirelman: Libros en idiomas extranjerosFormat: Tapa dura. History and Reform. Author: Kam C.

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In: KAM Theory and Semiclassical Approximations to Eigenfunctions. Ergebnisse der Mathematik und ihrer Grenzgebiete (3. Folge A Series of. This book provides a comprehensive introduction to the theoretical foundations of quantum tunneling, stressing the basic physics underlying the applications.

The topics addressed include exponential and nonexponential decay processes and the application of scattering theory to tunneling problems. In addition to the Schrödinger equation approach, the path integral.

It is important to realize that the semiclassical approximation has to do with how close F is to the path integral around the classical path. Any path integral can be written in the form of Eq.(1).

The semi-classical approximation then is an approximation to F. The general formula for F in semiclassical approximation is given at the end of.

Systems in an Annulus.- Notes to Chapter I.- II. KAM Theorems.- 9. The KAM Torus.- KAM Set.- The KAM Theorem in an Annulus.- Near a Torus.- Near a Periodic Motion.- Near the Boundary of Planar Convex Billiards.- The Robustness of a KAM Set.- Notes to Chapter II.- III.

Beyond the Tori.- General Picture of. Get this from a library. KAM Theory and Semiclassical Approximations to Eigenfunctions. [Vladimir F Lazutkin] -- It is a surprising fact that so far almost no books have been published on KAM theory.

The first part of this book seems to be the first monographic exposition of this subject, despite the fact that. Books. Publishing Support. Login. Ciocci M-C, Litvak-Hinenzon A and Broer H W Survey on dissipative KAM theory including quasi-periodic bifurcation theory Geometric Mechanics and Symmetry.

Lazutkin V F KAM Theory and Semiclassical Approximations to Eigenfunctions (Berlin: Springer) Crossref. Get this from a library. KAM theory and semiclassical approximations to eigenfunctions.

[Vladimir Fedorovich Lazutkin]. K-Theory of Finite Groups and Orders; K-Theory, Arithmetic and Geometry; K-theory and Homological Algebra; K. O. Mbadiwe; K. Waibels Leitfaden für die Prüfungen der Hebammen; K3 Surfaces and Their Moduli; KAFKA. Einbahnstraße zur Hölle; KALKULIERTE FLEXIBILITÄT; KAM Theory and Semiclassical Approximations to Eigenfunctions.KAM theory and semiclassical approximations to eigenfunctions.

With an addendum by A. I. Shnirelman KAM Theory and Semiclassical Approximations to Eigenfunctions. Book. Jan ; Vladimir F.KAM Theory and Semiclassical Approximations to Eigenfunctions Asymptotic Rayleigh-Schrödinger perturbation theory for discrete eigenvalues is developed systematically in .