Mathematical Problems in Quantum Physics
About this Title
Federico Bonetto, Georgia Institute of Technology, Atlanta, GA, David Borthwick, Emory University, Atlanta, GA, Evans Harrell, Georgia Institute of Technology, Atlanta, GA and Michael Loss, Georgia Institute of Technology, Atlanta, GA, Editors
Publication: Contemporary Mathematics
Publication Year: 2018; Volume 717
ISBNs: 978-1-4704-3681-0 (print); 978-1-4704-4939-1 (online)
This volume contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held from October 8–11, 2016, at the Georgia Institute of Technology, Atlanta, Georgia.
In recent years, a number of new frontiers have opened in mathematical physics, such as many-body localization and Schrödinger operators on graphs. There has been progress in developing mathematical techniques as well, notably in renormalization group methods and the use of Lieb–Robinson bounds in various quantum models.
The aim of this volume is to provide an overview of some of these developments. Topics include random Schrödinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory. A number of articles are devoted to the very active area of Schrödinger operators on graphs and general spectral theory of Schrödinger operators. Some of the articles are expository and can be read by an advanced graduate student.
Graduate students and research mathematicians interested in current developments in mathematical physics.
Table of Contents
- Rupert L. Frank, Phan Thành Nam and Hanne Van Den Bosch – A short proof of the ionization conjecture in Müller theory
- Marcello Porta – Mean field dynamics of interacting fermionic systems
- Houssam Abdul-Rahman, Robert Sims and Günter Stolz – Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches
- John Z. Imbrie – The lattice Anderson model with discrete disorder
- Vieri Mastropietro – Interacting fermions with quasi-random disorder
- M. Correggi, D. Lundholm and N. Rougerie – Local density approximation for almost-bosonic anyons
- Bruno Nachtergaele, Robert Sims and Amanda Young – Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
- Jens Bolte and George Garforth – Solvable models of interacting $n$-particle systems on quantum graphs
- Ram Band and August J. Krueger – Nonlinear Sturm oscillation: From the interval to a star
- Claudio Cacciapuoti – Existence of the ground state for the NLS with potential on graphs
- Vladimir Rabinovich – Fredholm theory of differential operators on periodic graphs
- Pavel Exner and Vladimir Lotoreichik – Optimization of the lowest eigenvalue for leaky star graphs
- Vincent Bruneau and Georgi Raikov – Local eigenvalue asymptotics of the perturbed Krein Laplacian
- Per von Soosten and Simone Warzel – Singular spectrum and recent results on hierarchical operators
- David Auckly and Peter Kuchment – On Parseval frames of exponentially decaying composite Wannier functions
- M. Ballesteros, N. Crawford, M. Fraas, J. Fröhlich and B. Schubnel – Non-demolition measurements of observables with general spectra
- Pieter Naaijkens – Subfactors and quantum information theory
- Rainer Dick – Dressing up for length gauge: Mathematical aspects of a debate in quantum optics
- Alain Joye and Marco Merkli – Random phase infinite coherent states: Construction and dynamics
- Marco Merkli – Effective evolution of open dimers