Multiscale Methods in Quantum Mechanics

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.

This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. 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.

Preface.
- Organic Molecules and Decoherence Experiments in a Molecule Interferometer.
- Colored Hofstadter Butterflies.
- Semiclassical Normal Forms.
- On the Exit Statistics Theorem of Many-particle Quantum Scattering.
- Two-scale Wigner Measures and the Landau-Zener Formulas.
- Stability of Three- and Four-Body Coulomb Systems.- Almost Invariant Subspaces for Quantum Evolutions.
- Nonlinear Asymptotics for Quantum Out-of-Equilibrium 1D Systems: Reduced Models and Algorithms.
- Decoherence-induced Classical Properties in Infinite Quantum Systems.
- Classical versus Quantum Structures: The Case of Pyramidal Molecules.
- On the Quantum Boltzmann Equation.
- Remarks on Time-dependent Schrödinger Equations, Bound States, and Coherent States.
- Nonlinear Time-dependent Schrödinger Equation with Double Well Potential.
- Classical and Quantum: Some Mutual Clarifications.
- Localization and Delocalization for Nonstationary Models.
- On a Rigorous Proof of the Joos-Zeh Formula for Decoherence in a Two-body Problem.
- Propagation of Wigner Functions for the Schrödinger Equation with a Perturbed Periodic Potential.