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Mathematical Physics of Quantum Mechanics [2006]

12
Stability of Multi-Phase Equilibria
1
Introduction
5
Solving the Ten Martini Problem
17
Swimming Lessons for Microbots
19
Landau-Zener Formulae from Adiabatic Transition Histories
33
Scattering Theory of Dynamic Electrical Transport
45
The Landauer-Büttiker Formula and Resonant Quantum Transport
55
Point Interaction Polygons: An Isoperimetric Problem
65
Limit Cycles in Quantum Mechanics
79
Cantor Spectrum for Quasi-Periodic Schrödinger Operators
95
Adiabatic Theorems and Reversible Isothermal Processes
107
Quantum Massless Field in 1+1 Dimensions
149
Ordering of Energy Levels in Heisenberg Models and Applications
171
Interacting Fermions in 2 Dimensions
179
On the Essential Spectrum of the Translation Invariant Nelson Model
199
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
217
Long Time Behaviour to the Schrödinger–Poisson–X<Superscript>α</Superscript> Systems
233
Towards the Quantum Brownian Motion
259
Bose-Einstein Condensation and Superradiance
279
Derivation of the Gross-Pitaevskii Hierarchy
295
Towards a Microscopic Derivation of the Phonon Boltzmann Equation
307
On the Quantization of Hall Currents in Presence of Disorder
325
Equality of the Bulk and Edge Hall Conductances in 2<Emphasis Type="Italic">D</Emphasis>
333
Generic Subsets in Spaces of Measures and Singular Continuous Spectrum
343
Low Density Expansion for Lyapunov Exponents
351
Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles
367
Recent Results on Quantum Map Eigenstates
383
Level Repulsion and Spectral Type for One-Dimensional Adiabatic Quasi-Periodic Schrödinger Operators
403
Low Lying Eigenvalues of Witten Laplacians and Metastability (After Hel.er-Klein-Nier and Helffer-Nier)
417
The Mathematical Formalism of a Particle in a Magnetic Field
435
Fractal Weyl Law for Open Chaotic Maps
451
Spectral Shift Function for Magnetic Schrödinger Operators
467
Counting String/M Vacua
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