Mathematical Physics of Quantum Mechanics: Selected and Refereed Lectures from QMath9

Introduction....Pages 1-1
Front Matter....Pages I-XXI
Solving the Ten Martini Problem....Pages 5-16
Swimming Lessons for Microbots....Pages 17-17
Landau-Zener Formulae from Adiabatic Transition Histories....Pages 19-32
Scattering Theory of Dynamic Electrical Transport....Pages 33-44
The Landauer-Büttiker Formula and Resonant Quantum Transport....Pages 45-53
Point Interaction Polygons: An Isoperimetric Problem....Pages 55-64
Limit Cycles in Quantum Mechanics....Pages 65-78
Cantor Spectrum for Quasi-Periodic Schrödinger Operators....Pages 79-91
Front Matter....Pages I-XXI
Adiabatic Theorems and Reversible Isothermal Processes....Pages 95-105
Quantum Massless Field in 1+1 Dimensions....Pages 107-127
Stability of Multi-Phase Equilibria....Pages 129-148
Ordering of Energy Levels in Heisenberg Models and Applications....Pages 149-170
Interacting Fermions in 2 Dimensions....Pages 171-178
On the Essential Spectrum of the Translation Invariant Nelson Model....Pages 179-195
Front Matter....Pages I-XXI
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice....Pages 199-215
Long Time Behaviour to the Schrödinger–Poisson–X α Systems....Pages 217-232
Towards the Quantum Brownian Motion....Pages 233-257
Bose-Einstein Condensation and Superradiance....Pages 259-278
Derivation of the Gross-Pitaevskii Hierarchy....Pages 279-293
Front Matter....Pages I-XXI
Towards a Microscopic Derivation of the Phonon Boltzmann Equation....Pages 295-304
Front Matter....Pages I-XXI
On the Quantization of Hall Currents in Presence of Disorder....Pages 307-323
Equality of the Bulk and Edge Hall Conductances in 2 D ....Pages 325-332
Generic Subsets in Spaces of Measures and Singular Continuous Spectrum....Pages 333-341
Low Density Expansion for Lyapunov Exponents....Pages 343-350
Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles....Pages 351-364
Front Matter....Pages I-XXI
Recent Results on Quantum Map Eigenstates....Pages 367-381
Level Repulsion and Spectral Type for One-Dimensional Adiabatic Quasi-Periodic Schrödinger Operators....Pages 383-402
Low Lying Eigenvalues of Witten Laplacians and Metastability (After Hel.er-Klein-Nier and Helffer-Nier)....Pages 403-415
The Mathematical Formalism of a Particle in a Magnetic Field....Pages 417-434
Fractal Weyl Law for Open Chaotic Maps....Pages 435-450
Spectral Shift Function for Magnetic Schrödinger Operators....Pages 451-465
Counting String/M Vacua....Pages 467-483