This proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.
Commutator methods for N-body Schrödinger operators.- Resolvent estimates and resonance free regions for Schrödinger operators with matrix-valued potentials.- One-dimensional discrete Anderson model in a decaying random potential: From a.c. spectrum to dynamical localization.- On non-selfadjoint operators with finite discrete spectrum.- Pseudo-differential perturbations of the Landau Hamiltonian.- Semiclassical surface wave tomography of isotropic media.- Persistence of point spectrum for perturbations of one-dimensional operators with discrete spectra.- Resonances for a system of Schrödinger operators above an energy-level crossing.- Nonexistence result for wave operators in massive relativistic system.- Quantized calculus for perturbed massive Dirac operator on noncommutative Euclidian space.- On the explicit semiclassical limiting eigenvalue (resonance) distribution for the Zeeman (Stark) hydrogen atom Hamiltonian.- Negative spectrum of the Robin Laplacian.- On some integral operators appearing in scattering theory, and their resolutions.- The strong Scott conjecture: The density of heavy atoms close to the nucleous.
Pablo Miranda is a Professor at the University of Santiago de Chile. He graduated from the University of Chile (2011) and did postdoctoral studies at the Institute of Physics, Catholic University of Chile and at the Mittag-Leffler Institute. His current research interests include magnetic Schrödinger operators, resonances in quantum systems and spectral shift function theory.
Nicolas Popoff is an Assistant Professor at the Institut de Mathématiques de Bordeaux, France. He got his PhD in 2012 from the University of Rennes 1, France, under the supervision of Virginie Bonnaillie-Noël and Monique Dauge. He held a teaching position at the University of Rennes and did postdoc studies with the Quantum Dynamics and Spectral Analysis team at the Center of Theoretical Physics of the University of Aix-Marseille. His research interests include spectral theory, PDE, mathematical physics and numerical analysis.
Georgi Raikov obtained his PhD in Mathematical Physics at Leningrad (St. Petersburg) State University, Russia, in 1986, and a higher doctoral degree D.Sc. in Mathematics in 1992 at the Bulgarian Academy of Science where he worked in the period 1987-2000. Since 2001 Georgi Raikov has been working in Chile, and at the moment he is a Full Professor at the Faculty of Mathematics of the Catholic University of Chile. His research areas are analysis, partial differential equations, mathematical physics, spectral and scattering theory of self-adjoint operators.
