Spectral Theory and Mathematical Physics

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics.

It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

Features expert and well-presented survey articles which start from basic facts and reach the forefront of research Presents new results in original and authoritative research papers, thematically complementing the surveys Highlights the research of the Chilean group working in the field of spectral theory, as well as of its collaborators from all over the world

Inhalt
Preface.- Lower bounds for sojourn time in a simple shape resonance model.- Spectral properties for Hamiltonians of weak interactions.- Magnetic Laplacian in sharp three-dimensional cones.- Spectral clusters for magnetic exterior problems.- The spectral shift function and the Witten index.- Stahl's theorem (aka BMV conjecture): insights and intuition on its proof.- Some estimates regarding integrated density of states for random Schrödingeroperator with decaying random potentials.- Boundary values of resolvents of self-adjoint operators in Krein spaces and applications to the Klein-Gordon equation.- Levinson's theorem: an index theorem in scattering theory.- Counting function of magnetic resonances for non-definite sign perturbations.- Harmonic analysis and random Schrödinger operators.