Multiscale Methods in Quantum Mechanics

1. Front Matter

   Pages i-ix

   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

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

• Potential
• Quantum mechanics
• Schrödinger equation
• algorithm
• algorithms
• mechanics
• stability
• statistics

"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

• Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany

  Philippe Blanchard

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

  Gianfausto Dell’Antonio

Policies and ethics