Contemporary Mathematics
Volume: 717;
2018;
338 pp;
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Mathematical Problems in Quantum Physics
Share this pageEdited by Federico Bonetto; David Borthwick; Evans Harrell; Michael Loss
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.
Readership
Graduate students and research mathematicians interested in current developments in mathematical physics.
Table of Contents
Mathematical Problems in Quantum Physics
- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- A short proof of the ionization conjecture in Müller theory 18
- Mean field dynamics of interacting fermionic systems 1320
- Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches 3138
- The lattice Anderson model with discrete disorder 4956
- Interacting fermions with quasi-random disorder 6572
- Local density approximation for almost-bosonic anyons 7784
- Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems 93100
- Solvable models of interacting 𝑛-particle systems on quantum graphs 117124
- Nonlinear Sturm oscillation: From the interval to a star 129136
- Existence of the ground state for the NLS with potential on graphs 155162
- Fredholm theory of differential operators on periodic graphs 173180
- Optimization of the lowest eigenvalue for leaky star graphs 187194
- Local eigenvalue asymptotics of the perturbed Krein Laplacian 197204
- Singular spectrum and recent results on hierarchical operators 215222
- On Parseval frames of exponentially decaying composite Wannier functions 227234
- Non-demolition measurements of observables with general spectra 241248
- Subfactors and quantum information theory 257264
- 1. Introduction 257264
- 2. Quantum channels and operator algebras 259266
- 3. Distinguishing states and relative entropy 262269
- 4. Subfactors, conditional expectations, and Jones index 263270
- 5. Wiretap channels and private classical capacity 265272
- 6. Examples: abelian quantum double models and CFT 267274
- 7. Finite dimensional approximation 271278
- References 277284
- Dressing up for length gauge: Mathematical aspects of a debate in quantum optics 281288
- 1. Introduction 281288
- 2. Dipole approximation and the transition to length gauge 286293
- 3. Switching to length gauge only for particular species 290297
- 4. Analytic differences between velocity gauge and length gauge 291298
- 5. Acceleration gauge and shifts in phase space 295302
- 6. Conclusions 299306
- 7. Appendix: Energy and momentum in Coulomb gauge 302309
- References 304311
- Random phase infinite coherent states: Construction and dynamics 307314
- Effective evolution of open dimers 323330
- Back Cover Back Cover1346