Full Description
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.
Contents
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.
