Multiscale Methods in Quantum Mechanics: Theory and Experiment

✍ Scribed by M. Arndt, L. Hackermüller, K. Hornberger (auth.), Philippe Blanchard, Gianfausto Dell’Antonio (eds.)

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 222
• Series: Trends in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-ix
Organic Molecules and Decoherence Experiments in a Molecule Interferometer....Pages 1-10
Colored Hofstadter Butterflies....Pages 11-22
Semiclassical Normal Forms....Pages 23-39
On the Exit Statistics Theorem of Many-particle Quantum Scattering....Pages 41-58
Two-scale Wigner Measures and the Landau—Zener Formulas....Pages 59-68
Stability of Three-and Four-Body Coulomb Systems....Pages 69-81
Almost Invariant Subspaces for Quantum Evolutions....Pages 83-97
Nonlinear Asymptotics for Quantum Out-of-Equilibrium 1D Systems: Reduced Models and Algorithms....Pages 99-111
Decoherence-induced Classical Properties in Infinite Quantum Systems....Pages 113-118
Classical versus Quantum Structures: The Case of Pyramidal Molecules....Pages 119-127
On the Quantum Boltzmann Equation....Pages 129-138
Remarks on Time-dependent Schrödinger Equations, Bound States, and Coherent States....Pages 139-158
Nonlinear Time-dependent Schrödinger Equations with Double-Well Potential....Pages 159-173
Classical and Quantum: Some Mutual Clarifications....Pages 175-184
Localization and Delocalization for Nonstationary Models....Pages 185-195
On a Rigorous Proof of the Joos–Zeh Formula for Decoherence in a Two-body Problem....Pages 197-205
Propagation of Wigner Functions for the Schrödinger Equation with a Perturbed Periodic Potential....Pages 207-220

✦ Subjects

Applications of Mathematics;Mathematical Methods in Physics;Quantum Physics;Quantum Information Technology, Spintronics;Quantum Optics;Appl.Mathematics/Computational Methods of Engineering