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Birkhäuser

Multiscale Methods in Quantum Mechanics

Theory and Experiment

  • Conference proceedings
  • © 2004

Overview

Editors:
  1. Philippe Blanchard

    1. Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany

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    You can also search for this editor in PubMed   Google Scholar

  2. Gianfausto Dell’Antonio

    1. Dipartimento di Matematica, Università degli Studi di Roma “La Sapienza”, Roma, Italy

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • First text totally devoted to multiscale methods as applied to various areas of physics and to the relative developments in mathematics
  • Very timely in view of recent theoretical and experimental progress
  • Aimed at mathematical physicists, theoretical physicists, applied mathematicians, and experimental physicists working in such areas as decoherence, quantum information, and quantum optics

Part of the book series: Trends in Mathematics (TM)

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Table of contents (17 papers)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Organic Molecules and Decoherence Experiments in a Molecule Interferometer

    • M. Arndt, L. Hackermüller, K. Hornberger, A. Zeilinger
    Pages 1-10

  3. Colored Hofstadter Butterflies

    • J. E. Avron
    Pages 11-22

  4. Semiclassical Normal Forms

    • D. Bambusi
    Pages 23-39

  5. On the Exit Statistics Theorem of Many-particle Quantum Scattering

    • D. Dürr, S. Teufel
    Pages 41-58

  6. Two-scale Wigner Measures and the Landau—Zener Formulas

    • C. Fermanian Kammerer, P. Gérard
    Pages 59-68

  7. Stability of Three-and Four-Body Coulomb Systems

    • A. Martin
    Pages 69-81

  8. Almost Invariant Subspaces for Quantum Evolutions

    • G. Nenciu
    Pages 83-97

  9. Nonlinear Asymptotics for Quantum Out-of-Equilibrium 1D Systems: Reduced Models and Algorithms

    • F. Nier, M. Patel
    Pages 99-111

  10. Decoherence-induced Classical Properties in Infinite Quantum Systems

    • R. Olkiewicz
    Pages 113-118

  11. Classical versus Quantum Structures: The Case of Pyramidal Molecules

    • C. Presilla, G. Jona-Lasinio, C. Toninelli
    Pages 119-127

  12. On the Quantum Boltzmann Equation

    • M. Pulvirenti
    Pages 129-138

  13. Remarks on Time-dependent Schrödinger Equations, Bound States, and Coherent States

    • D. Robert
    Pages 139-158

  14. Nonlinear Time-dependent Schrödinger Equations with Double-Well Potential

    • A. Sacchetti
    Pages 159-173

  15. Classical and Quantum: Some Mutual Clarifications

    • V. Scarani
    Pages 175-184

  16. Localization and Delocalization for Nonstationary Models

    • P. Stollmann
    Pages 185-195

  17. On a Rigorous Proof of the Joos–Zeh Formula for Decoherence in a Two-body Problem

    • A. Teta
    Pages 197-205

  18. Propagation of Wigner Functions for the Schrödinger Equation with a Perturbed Periodic Potential

    • S. Teufel, G. Panati
    Pages 207-220
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Keywords

About this book

In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics. In view of this progress, this volume is very timely; it is the first text totally devoted to multiscale methods as applied to various areas of physics and to the relative developments in mathematics.

The book is aimed at mathematical physicists, theoretical physicists, applied mathematicians, and experimental physicists working in such areas as decoherence, quantum information, and quantum optics.

Contributors: M. Arndt; J.E. Avron; D. Bambusi; D. Dürr; C. Fermanian Kammerer; P. Gerard; L. Hackermüller; K. Hornberger; G. Jona-Lasinio; A. Martin; G. Nenciu; F. Nier; R. Olkiewicz; G. Panati; M. Patel; C. Presilla; M. Pulvirenti; D. Robert; A. Sacchetti; V. Scarani; P. Stollmann; A. Teta; S. Teufel; C. Toninelli; and A. Zeilinger

Reviews

"During recent years spectacular progress has been made in experimentally testing the foundations of quantum mechanics. This development has been complemented by significant theoretical advances in the mathematical description of complex quantum mechanical systems mainly based on so called mutiscale methods" ---Monatshefte für Mathematik

Editors and Affiliations

  • Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany

    Philippe Blanchard

  • Dipartimento di Matematica, Università degli Studi di Roma “La Sapienza”, Roma, Italy

    Gianfausto Dell’Antonio

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