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Asch J., Joye A. (Eds.) Mathematical Physics of Quantum Mechanics. Selected and Refereed Lectures from QMath9

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Asch J., Joye A. (Eds.) Mathematical Physics of Quantum Mechanics. Selected and Refereed Lectures from QMath9
Springer, 2006. — 462 p. — (Lecture Notes in Physics 690). — ISBN: 978-3-540-34273-1, 978-3-642-42157-0, 978-3-540-31026-6.
At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.
Introduction
Introduction
Quantum Dynamics and Spectral Theory
Solving the Ten Martini Problem
Swimming Lessons for Microbots
Landau-Zener Formulae from Adiabatic Transition Histories
Scattering Theory of Dynamic Electrical Transport
The Landauer-Büttiker Formula and Resonant Quantum Transport
Point Interaction Polygons: An Isoperimetric Problem
Limit Cycles in Quantum Mechanics
Cantor Spectrum for Quasi-Periodic Schrödinger Operators
Quantum Field Theory and Statistical Mechanics
Adiabatic Theorems and Reversible Isothermal Processes
Quantum Massless Field in 1+1 Dimensions
Stability of Multi-Phase Equilibria
Ordering of Energy Levels in Heisenberg Models and Applications
Interacting Fermions in 2 Dimensions
On the Essential Spectrum of the Translation Invariant Nelson Model
Quantum Kinetics and Bose-Einstein Condensation
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
Long Time Behaviour to the Schrödinger–Poisson–Xα Systems
Towards the Quantum Brownian Motion
Bose-Einstein Condensation and Superradiance
Derivation of the Gross-Pitaevskii Hierarchy
Towards a Microscopic Derivation of the Phonon Boltzmann Equation
Disordered Systems and Random Operators
On the Quantization of Hall Currents in Presence of Disorder
Equality of the Bulk and Edge Hall Conductances in 2D
Generic Subsets in Spaces of Measures and Singular Continuous Spectrum
Low Density Expansion for Lyapunov Exponents
Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles
Semiclassical Analysis and Quantum Chaos
Recent Results on Quantum Map Eigenstates
Level Repulsion and Spectral Type for One-Dimensional Adiabatic Quasi-Periodic Schrödinger Operators
Low Lying Eigenvalues of Witten Laplacians and Metastability (After Helffer-Klein-Nier and Helffer-Nier)
The Mathematical Formalism of a Particle in a Magnetic Field
Fractal Weyl Law for Open Chaotic Maps
Spectral Shift Function for Magnetic Schrödinger Operators
Counting String/M Vacua
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