Volume 690 2006

Mathematical Physics of Quantum Mechanics

Selected and Refereed Lectures from QMath9

Editors:

ISBN: 978-3-540-31026-6 (Print) 978-3-540-34273-1 (Online)

Table of contents (33 chapters)

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  1. Introduction

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      Book Chapter

      Pages 1-1

      Introduction

  2. Quantum Dynamics and Spectral Theory

    1. Front Matter

      Pages I-XXI

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      Book Chapter

      Pages 5-16

      Solving the Ten Martini Problem

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      Book Chapter

      Pages 17-17

      Swimming Lessons for Microbots

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      Book Chapter

      Pages 19-32

      Landau-Zener Formulae from Adiabatic Transition Histories

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      Book Chapter

      Pages 33-44

      Scattering Theory of Dynamic Electrical Transport

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      Book Chapter

      Pages 45-53

      The Landauer-Büttiker Formula and Resonant Quantum Transport

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      Book Chapter

      Pages 55-64

      Point Interaction Polygons: An Isoperimetric Problem

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      Book Chapter

      Pages 65-78

      Limit Cycles in Quantum Mechanics

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      Book Chapter

      Pages 79-91

      Cantor Spectrum for Quasi-Periodic Schrödinger Operators

  3. Quantum Field Theory and Statistical Mechanics

    1. Front Matter

      Pages I-XXI

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      Book Chapter

      Pages 95-105

      Adiabatic Theorems and Reversible Isothermal Processes

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      Book Chapter

      Pages 107-127

      Quantum Massless Field in 1+1 Dimensions

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      Book Chapter

      Pages 129-148

      Stability of Multi-Phase Equilibria

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      Book Chapter

      Pages 149-170

      Ordering of Energy Levels in Heisenberg Models and Applications

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      Book Chapter

      Pages 171-178

      Interacting Fermions in 2 Dimensions

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      Book Chapter

      Pages 179-195

      On the Essential Spectrum of the Translation Invariant Nelson Model

  4. Quantum Kinetics and Bose-Einstein Condensation

    1. Front Matter

      Pages I-XXI

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      Book Chapter

      Pages 199-215

      Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice

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      Book Chapter

      Pages 217-232

      Long Time Behaviour to the Schrödinger–Poisson–Xα Systems

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      Book Chapter

      Pages 233-257

      Towards the Quantum Brownian Motion

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      Book Chapter

      Pages 259-278

      Bose-Einstein Condensation and Superradiance

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      Book Chapter

      Pages 279-293

      Derivation of the Gross-Pitaevskii Hierarchy

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