This book is the first volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to semiclassical analysis, quantum field theory, Schrödinger and Dirac operators and open quantum systems
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 spinboson 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.
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 Universitą 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).
