Mathematical problems in quantum physics : QMATH13 : Mathematical results in quantum physics, October 8-11, 2016, Georgia Institute of Technology, Atlanta, Georgia

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. Title Page......Page 2 Copyright......Page 3 Contents......Page 4 Preface......Page 6 A short proof of the ionization conjecture in Müller theory • Rupert L. Frank, Phan Thành Nam, and Hanne Van Den Bosch......Page 8 Mean field dynamics of interacting fermionic systems • Marcello Porta......Page 20 Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches • Houssam Abdul-Rahman, Robert Sims, and Günter Stolz......Page 38 The lattice Anderson model with discrete disorder • John Z. Imbrie......Page 56 Interacting fermions with quasi-random disorder • Vieri Mastropietro......Page 72 Local density approximation for almost-bosonic anyons • M. Correggi, D. Lundholm, and N. Rougerie......Page 84 Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems • Bruno Nachtergaele, Robert Sims, and Amanda Young......Page 100 Solvable models of interacting n-particle systems on quantum graphs • Jens Bolte and George Garforth......Page 124 Nonlinear Sturm oscillation: From the interval to a star • Ram Band and August J. Krueger......Page 136 Existence of the ground state for the NLS with potential on graphs • Claudio Cacciapuoti......Page 162 Fredholm theory of differential operators on periodic graphs • Vladimir Rabinovich......Page 180 Optimization of the lowest eigenvalue for leaky star graphs • Pavel Exner and Vladimir Lotoreichik......Page 194 Local eigenvalue asymptotics of the perturbed Krein Laplacian • Vincent Bruneau and Georgi Raikov......Page 204 Singular spectrum and recent results on hierarchical operators • Per von Soosten and Simone Warzel......Page 222 On Parseval frames of exponentially decaying composite Wannier functions • David Auckly and Peter Kuchment......Page 234 Non-demolition measurements of observables with general spectra • M. Ballesteros, N. Crawford, M. Fraas, J. Fröhlich, and B. Schubnel......Page 248 Subfactors and quantum information theory • Pieter Naaijkens......Page 264 Dressing up for length gauge: Mathematical aspects of a debate in quantum optics • Rainer Dick......Page 288 Random phase infinite coherent states: Construction and dynamics • Alain Joye and Marco Merkli......Page 314 Effective evolution of open dimers • Marco Merkli......Page 330 A Short Proof Of The Ionization Conjecture In Müller Theory / Rupert L. Frank, Phan Thành Nam And Hanne Van Den Bosch -- Mean-field Dynamics Of Interacting Fermionic Systems / Marcello Porta -- Correlations In Disordered Quantum Harmonic Oscillator Systems : The Effects Of Excitations And Quantum Quenches / Houssam Abdul-rahman, Robert Sims And Gunter Stolz -- The Lattice Anderson Model With Discrete Disorder / John Z. Imbrie -- Interacting Fermions With Quasi-random Disorder / Vieri Mastropietro -- Local Density Approximation For Almost-bosonic Anyons / M. Correggi, D. Lundholm And N. Rougerie -- Lieb-robinson Bounds, The Spectral Flow, And Stability Of The Spectral Gap For Lattice Fermion Systems / Bruno Nachtergaele, Robert Sims And Amanda Young -- Solvable Models Of Interacting N-particle Systems On Quantum Graphs / Jens Bolte And George Garforth -- Nonlinear Sturm Oscillation : From The Interval To A Star / Ram Band And August J. Krueger-- Existence Of The Ground State For The Nls With Potential On Graphs / Claudio Cacciapuoti -- Fredholm Theory Of Differential Operators On Periodic Graphs / Vladimir Rabinovich -- Optimization Of The Lowest Eigenvalue For Leaky Star Graphs / Pavel Exner And Vladimir Lotoreichik -- Local Eigenvalue Asymptotics Of The Perturbed Krein Laplacian / Vincent Bruneau And Georgi Raikov -- Singular Spectrum And Recent Results On Hierarchical Operators / Per Von Soosten And Simone Warzel -- On Parseval Frames Of Exponentially Decaying Composite Wannier Functions / David Auckly And Peter Kuchment -- Non-demolition Measurements Of Observables With General Spectra / M. Ballesteros, N. Crawford, M. Fraas, J. Frohlich And B. Schubnel -- Subfactors And Quantum Information Theory / Pieter Naaijkens -- Dressing Up For Length Gauge : Mathematical Aspects Of A Debate In Quantum Optics / Rainer Dick -- Random Phase Infinite Coherent States : Construction And Dynamics / Alain Joye And Marco Merkli-- Effective Evolution Of Open Dimers / Marco Merkli. Federico Bonetto, David Borthwick, Evans Harrell, Michael Loss, Editors. Place Of Publication From Publisher's Website. Includes Bibliographical References. Contains the proceedings of the QMATH13: Mathematical Results in Quantum Physics conference, held in October 2016. Topics include random Schrodinger operators, many-body fermionic systems, atomic systems, effective equations, and applications to quantum field theory.