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Product Code:  CONM/717 
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Electronic ISBN:  9781470449391 
Product Code:  CONM/717.E 
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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