Macroscopic Limits of Quantum Systems: Munich, Germany, March 30 - April 1, 2017 (Springer Proceedings in Mathematics & Statistics Book 270)

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 achievements of Herbert Spohn and his reception of the Max Planck Medal. Front Matter ....Pages i-viii Kinetic Theory and Thermalization of Weakly Interacting Fermions (Jani Lukkarinen)....Pages 1-28 The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator (Rupert L. Frank, Christian Hainzl)....Pages 29-62 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 Mean-Field Evolution of Fermions with Singular Interaction (Chiara Saffirio)....Pages 81-99 Recent Advances in the Theory of Bogoliubov Hamiltonians (Marcin Napiórkowski)....Pages 101-121 Multi-scale Analysis in the Occupation Numbers of Particle States: An Application to Three-Modes Bogoliubov Hamiltonians (Alessandro Pizzo)....Pages 123-144 Blow-Up Profile of Rotating 2D Focusing Bose Gases (Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie)....Pages 145-170 Gross–Pitaevskii Evolution for Bose–Einstein Condensates (Benjamin Schlein)....Pages 171-184 Mean-Field Limits of Particles in Interaction with Quantized Radiation Fields (Nikolai Leopold, Peter Pickl)....Pages 185-214 Taking Inspiration from Quantum-Wave Analogies—Recent Results for Photonic Crystals (Max Lein)....Pages 215-242 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 achievements of Herbert Spohn and his reception of the Max Planck Medal.-- Provided by publisher