Mathematical physics of quantum mechanics: selected and refereed lectures from QMath9

Joachim Asch, Alain Joye (auth.), Joachim Asch, Alain Joye (eds.)3540310266, 9783540310266, 9783540342731

At the QMath9 meeting, young scientists learn about the state of the art in the mathematical physics of quantum systems. Based on that event, this book offers a selection of outstanding articles written in pedagogical style comprising six sections which cover new techniques and recent results on spectral theory, statistical mechanics, Bose-Einstein condensation, random operators, magnetic Schrödinger operators and much more. For postgraduate students, Mathematical Physics of Quantum Systems serves as a useful introduction to the research literature. For more expert researchers, this book will be a concise and modern source of reference.

Table of contents :
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