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 Schrodinger 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 Schrodinger 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 Schrodinger operators on graphs and general spectral theory of Schrodinger operators. Some of the articles are expository and can be read by an advanced graduate student.
R. L. Frank, P. T. Nam, and H. Van Den Bosch, A short proof of the
ionization conjecture in Muller theory
M. Porta, Mean field dynamics of interacting fermionic systems
H. Abdul-Rahman, R. Sims, and G. Stolz, Correlations in disordered quantum
harmonic oscillator systems: The effects of excitations and quantum quenches
J. Z. Imbrie, The lattice Anderson model with discrete disorder
V. Mastropietro, Interacting fermions with quasi-random disorder
M. Correggi, D. Lundholm, and N. Rougerie, Local density approximation for
almost-bosonic anyons
B. Nachtergaele, R. Sims, and A. Young, Lieb-Robinson bounds, the spectral
flow, and stability of the spectral gap for lattice fermion systems
J. Bolte and G. Garforth, Solvable models of interacting $n$-particle systems
on quantum graphs
R. Band and A. J. Krueger, Nonlinear Sturm oscillation: From the interval to
a star
C. Cacciapuoti, Existence of the ground state for the NLS with potential on
graphs
V. Rabinovich, Fredholm theory of differential operators on periodic graphs
P. Exner and V. Lotoreichik, Optimization of the lowest eigenvalue for leaky
star graphs
V. Bruneau and G. Raikov, Local eigenvalue asymptotics of the perturbed Krein
Laplacian
P. von Soosten and S. Warzel, Singular spectrum and recent results on
hierarchical operators
D. Auckly and P. Kuchment, On Parseval frames of exponentially decaying
composite Wannier functions
M. Ballesteros, N. Crawford, M. Fraas, J. Frohlich, and B. Schubnel,
Non-demolition measurements of observables with general spectra
P. Naaijkens, Subfactors and quantum information theory
R. Dick, Dressing up for length gauge: Mathematical aspects of a debate in
quantum optics
A. Joye and M. Merkli, Random phase infinite coherent states: Construction
and dynamics
M. Merkli, Effective evolution of open dimers.
Federico Bonetto, Georgia Institute of Technology, Atlanta, GA.
David Borthwick, Emory University, Atlanta, GA.
Evans Harrell, Georgia Institute of Technology, Atlanta, GA.
Michael Loss, Georgia Institute of Technology, Atlanta, GA.
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