Advances in Quantum Mechanics

This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.

Prof Gianfausto Dell'Antonio’s research focuses on axiomatic quantum field theory, local field theory, mathematics of quantum mechanics, critical point theory, stochastic processes, singular interactions, and many-body problems. He graduated in theoretical physics in Milan, was research associate in Copenhagen (Niels Bohr institute), Zurich (ETH), and Evanson (Northwestern), then professor of theoretical physics in Naples and professor of rational mechanics and mathematical physics at La Sapienza Rome. He held visiting professorships at the IHES Paris, Courant Insitute NY, The University of Marseille Luminy, Bielefeld University (as a recipient of a von Humboldt prize), CERN, SISSA Trieste, and the Interdisciplinary Laboratory of the Accademia dei Lincei. He held also visiting positions at the IAS Princeton, Ecole Politechnique Paris, Paris Dauphine, Harvard University, and the Max Planck Institute in Munich. Dr Alessandro Michelangeli’s research is in the field at the interface between mathematical physics, functional analysis and non-linear dispersive PDE, and operator theory, with a special focus on the mathematical methods for quantum mechanical and condensed matter systems. He graduated in theoretical physics in Pisa and then mathematical physics at SISSA Trieste, held faculty positions at the LMU Munich and SISSA Trieste, and visiting positions at the University of Cambridge, SISSA Trieste, and Bilkent.