Week 1: 6th - 10th July 2020
Basic Techniques of Quantum Many-Body Physics
Monday: General Introduction and Tools: Reminder of advanced quantum mechanics: Coordinate and momentum representations of the Hilbert space, discrete bases, operators, Schrödinger equation, spin, isospin.
Tuesday: Second quantization: Fermions and bosons, Fock space, Wick theorem, equivalence between representations
Wednesday: Exact vs. Approximate Many-Body Methods. Foundations of EDF theory, reminders of electronic DFT, Ab initio and Configuration Interaction (CI) approaches, spontaneous symmetry breaking.
Thursday: Hartree-Fock (HF) theory: product states, density matrices, variational principle, Thouless theorem, Koopman’s theorem
Friday: Pairing correlations. BCS theory, pairing tensor, Hartree-Fock-Bogoliubov (HFB) theory
Week 2: 13th - 17th July 2020
Structure and Dynamics
Monday: Random Phase Approximation (RPA): Introduction to time-dependent Hartree-Fock (TDHF) theory, linear response, stability matrix
Tuesday: Multi-reference EDF I: Restoration of broken symmetries. Projectors, transition densities, kernels, VAP vs. PAV
Wednesday: Multi-reference EDF II: Configuration mixing. GCM, Hill-Wheeler equation, collective Schrödinger equation.
Thursday: Energy density functionals: general properties, pseudopotentials, phe- nomenological EDFs, pairing functionals
Friday: Practical Applications. Determination of EDF parameters, nuclear matter, observables
Week 3: 20th - 24th July 2020
Phenomenology and Applications
Monday: Time-dependent density functional theory. TDHF, TDHFB, TDSLDA, time- odd fields, dissipation.
Tuesday: Nuclear phenomenology: Nilsson orbitals, experimental observables (multi- pole moments, gamma spectroscopy, moments of inertia, etc.)
Wednesday: Modern theory of nuclear forces, EDFs and nuclear forces, connections with ab initio theory.
Thursday: Open questions in nuclear DFT: non-empirical functionals, inclusion of collective correlations, spectroscopy, solvers, UQ, applications (fission, fun- damental symmetries, astrophysics), etc.
Friday: Course summary, discussions