Multiscale Methods in Quantum Mechanics: Theory and Experiment (Trends in Mathematics)

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. 1 Organic Molecules and Decoherence Experiments in a Molecule Interferometer.- 2 Colored Hofstadter Butterflies.- 3 Semiclassical Normal Forms.- 4 On the Exit Statistics Theorem of Many-particle Quantum Scattering.- 5 Two-scale Wigner Measures and the Landau-Zener Formulas.- 6 Stability of Three-and Four-Body Coulomb Systems.- 7 Almost Invariant Subspaces for Quantum Evolutions.- 8 Nonlinear Asymptotics for Quantum Out-of-Equilibrium 1D Systems: Reduced Models and Algorithms.- 9 Decoherence-induced Classical Properties in Infinite Quantum Systems.- 10 Classical versus Quantum Structures: The Case of Pyramidal Molecules.- 11 On the Quantum Boltzmann Equation.- 12 Remarks on Time-dependent Schrdinger Equations, Bound States, and Coherent States.- 13 Nonlinear Time-dependent Schrdinger Equations with Double-Well Potential.- 14 Classical and Quantum: Some Mutual Clarifications.- 15 Localization and Delocalization for Nonstationary Models.- 16 On a Rigorous Proof of the Joos-Zeh Formula for Decoherence in a Two-body Problem.- 17 Propagation of Wigner Functions for the Schrdinger Equation with a Perturbed Periodic Potential.