Quantum Mathematics I

M. Correggi: Organizer of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, March-May 2022; Full Professor in Mathematical Physics since 2020 at Politecnico di Milano; Coordinator of the Ph.D. program on Mathematical Models and Methods in Engineering at Politecnico di Milano (2022 - 2024); Ph.D. in Mathematical Physics (SISSA, Trieste, 2004); 18 years of research experience after Ph.D.; Principal Investigator of a MIUR FIR grant of 1 million €; 46 publications in international peer-reviewed journals; Participant to more than 50 international events; More than 60 invited talks; Invited speaker at the XVIII International Congress on Mathematical Physics, Santiago de Chile, Chile; Invited speaker at the XXI Congresso dell'Unione Matematica Italiana, Pavia, Italia; Organizer of 14 international events (1 Intensive Period INdAM, 1 Nordita, 1 CMO/BIRS, 3 Schools MCQM & 1 EMS-IAMP School with more than 100 participants). M. Falconi: Organizer of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)" at Politecnico di Milano, March-May 2022; Associate Professor in Mathematical Physics since 2023 at Politecnico di Milano; Ph.D. in Analysis (Alma Mater Studiorum – Università di Bologna, 2012); 11 years of research experience after Ph.D.; 21 publications in international peer-reviewed journals; Participant to more than 30 international events; More than 20 invited talks; Organizer of 2 international events (1 Intensive Period INdAM, 1 Hausdorff Summer School).

Chapter 1. Introduction.- Chapter 2. Many-Body Quantum Mechanics.- Chapter 3. Two Comments on the Derivation of the Time-Dependent Hartree-Fock Equation.- Chapter 4. Bogoliubov Theory for Ultra Dilute Bose Gases.- Chapter 5. Derivation of the Ginzburg-Landau Theory for Interacting Fermions in a Trap.- Chapter 6. Energy expansions for dilute Bose gases from local condensation results: a review of known results.- Chapter 7. Bogoliubov theory for the dilute Fermi gas in three dimensions.- Chapter 8. Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with External Potentials.- Chapter 9. Trial states for Bose gases: singular scalings and non-integrable potentials.- Chapter 10. Bogoliubov Transformations Beyond Shale-Stinespring: Generic v* v for bosons.- Chapter 11. Thermodynamic Game and The Kac Limit in Quantum Lattices.- Chapter 12. Topological Polarization in disordered systems.- Chapter 13. Open Quantum Systems.- Chapter 14. On the AsymptoticsDynamics of Open Quantum Systems.- Chapter 15. Boson quadratic GKLS generators.- Chapter 16. Semiclassical Analysis.- Chapter 17. Some Remarks on Semiclassical Analysis on Two-Steps Nilmanifolds.- Chapter 18. Waves in a Random Medium: Endpoint Strichartz Estimates and Number Estimates.- Chapter 19. Quasi-Classical Spin Boson Models.- Chapter 20. On the Semiclassical Regularity of Thermal Equilibria.- Chapter 21. Invariant measures as probabilistic tools in the analysis of nonlinear ODEs & PDEs.- Chapter 22. Quantum Field Theory.- Chapter 23. An Evolution Equation Approach to Linear Quantum Field Theory.- Chapter 24. Renormalization of spin–boson interactions mediated by singular form factors:The Casimir-Polder effect for an approximate Pauli-Fierz model: the atom plus wall case.- Chapter 25. Dynamical Systems Involving Pseudo-Fermionic Operators and Generalized Quaternion Groups.- Chapter 26. Schroedinger and Dirac Operators.- Chapter 27. Spectral Asymptotics for Two-dimensional Dirac Operators in Thin Waveguides.- Chapter 28. Quadratic forms for Aharonov-Bohm Hamiltonians.- Chapter 29. On the magnetic Laplacian with a piecewise constant magnetic field in R3+.- Chapter 30. Quantum Systems at The Brink. - Chapter 31. Lowest Eigenvalue Asymptotics in Strong Magnetic Fields with Interior Singularities.- Chapter 32. Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions.