Mathematical Physics of Quantum Mechanics

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.

Klappentext

This selection of outstanding articles - an outgrowth of the QMath9 meeting for young scientists - covers new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and more. The book's pedagogical style makes it a useful introduction to the research literature for postgraduate students. For more expert researchers it will serve as a concise source of modern reference.

Inhalt

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-X? 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 Hel.er-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.