Macroscopic Limits of Quantum Systems

1. Front Matter

   Pages i-viii

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2. Kinetic Theory and Thermalization of Weakly Interacting Fermions

   • Jani Lukkarinen

   Pages 1-28

3. The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator

   • Rupert L. Frank, Christian Hainzl

   Pages 29-62

4. Effective Dynamics of Two Tracer Particles Coupled to a Fermi Gas in the High-Density Limit

   • Maximilian Jeblick, David Mitrouskas, Peter Pickl

   Pages 63-79

5. Mean-Field Evolution of Fermions with Singular Interaction

   • Chiara Saffirio

   Pages 81-99

6. Recent Advances in the Theory of Bogoliubov Hamiltonians

   • Marcin Napiórkowski

   Pages 101-121

7. Multi-scale Analysis in the Occupation Numbers of Particle States: An Application to Three-Modes Bogoliubov Hamiltonians

   • Alessandro Pizzo

   Pages 123-144

8. Blow-Up Profile of Rotating 2D Focusing Bose Gases

   • Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie

   Pages 145-170

9. Gross–Pitaevskii Evolution for Bose–Einstein Condensates

   • Benjamin Schlein

   Pages 171-184

10. Mean-Field Limits of Particles in Interaction with Quantized Radiation Fields

    • Nikolai Leopold, Peter Pickl

    Pages 185-214

11. Taking Inspiration from Quantum-Wave Analogies—Recent Results for Photonic Crystals

    • Max Lein

    Pages 215-242

12. The Localization Dichotomy for Gapped Periodic Systems and Its Relevance for Macroscopic Transport

    • Gianluca Panati

    Pages 243-257

Based on the workshop of the same name, this proceedings volume presents selected research investigating the mathematics of collective phenomena emerging from quantum theory at observable scales. Featured contributions from leading scientists provide a thorough overview of current and active research. Methods from functional analysis, spectral theory, renormalization group theory, and variational calculus are used to prove rigorous results in quantum physics. Topics include superconductivity and mathematical aspects of the BCS theory, the Jellium model and Bose-Einstein condensation, among others. Presenting technical details in an accessible way, this book serves as an introduction to research for advanced graduate students and is suitable for specialists in mathematical physics.

The workshop “Macroscopic Limits of Quantum Systems” was held over three days in the spring of 2017 at the Technical University of Munich. The conference celebrated the achievementsof Herbert Spohn and his reception of the Max Planck Medal.

• Quantum Systems
• Macroscopic Limits
• proceedings
• quantum theory
• bosonic systems
• fermionic systems
• superconductivity
• mathematical aspects of BCS theory
• Boltzmann-type equations
• theory of indirect measurements
• polaron model
• functional analysis
• spectral theory
• statistical mechanics
• variational calculus
• renormalization group techniques

• Institut für Theoretische, Physik Universität Leipzig, Leipzig, Germany

  Daniela Cadamuro

• Zentrum Mathematik, M5, Technische Universität München, Garching, Germany

  Maximilian Duell, Wojciech Dybalski

• UMPA UMR 5669 CNRS, École normale supérieure, Lyon, France

  Sergio Simonella

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