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

Joachim Asch, Alain Joye (auth.), Joachim Asch, Alain Joye (eds.)9783540310266, 3-540-31026-6

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