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Book DetailsContemporary MathematicsVolume: 717; 2018; 338 ppMSC: Primary 81; 82
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 manybody 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, manybody 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.
ReadershipGraduate students and research mathematicians interested in current developments in mathematical physics.

Table of Contents

Articles

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 AbdulRahman, 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 quasirandom disorder

M. Correggi, D. Lundholm and N. Rougerie — Local density approximation for almostbosonic anyons

Bruno Nachtergaele, Robert Sims and Amanda Young — LiebRobinson 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 — Nondemolition 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


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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 manybody 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, manybody 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.

Articles

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 AbdulRahman, 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 quasirandom disorder

M. Correggi, D. Lundholm and N. Rougerie — Local density approximation for almostbosonic anyons

Bruno Nachtergaele, Robert Sims and Amanda Young — LiebRobinson 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 — Nondemolition 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