13. Schrieffer-Wolff Transformation pt.3: Diagrammatology - Quantum Dynamics (Spring 2026)

[1]: S. Bravyi, D.P. DiVincenzo and D. Loss, Schrieffer–Wolff transformation for quantum many-body systems, Annals of Physics 326 , 2793 (2011), doi: https://doi.org/10.1016/j.aop.2011.06.... Division of Theoretical Physics of Institute of Physics, PAS presents: "Quantum Dynamics: an Overview" Time & Location: Spring 2026, Wednesdays at 10:00 CET, room 15/XV, Institute of Physics PAS Website: https://theory.ifpan.edu.pl/?class=25... Lecturer: Dr Piotr Szańkowski ([email protected]) Reading Materials: Available on the course website. Language: English COURSE OBJECTIVES: The course offers an overview of theoretical approaches to the description of _quantum dynamics_, from the basic exponential map generated by the system’s Hamiltonian, to the adiabatic theorem, and Green’s function methods. Our focus will be on a perturbation-theoretical approach—the likes of the Schrieffer–Wolff transformation and the Magnus expansion—that reveals the underlying structures of quantum dynamical laws, rather than on numerical methods meant only for efficient computation. Hence, the course will lean more toward the formalistic and mathematical side, but not overly so. ADMISSION REQUIREMENTS: Basic knowledge of quantum mechanics is expected. TEACHING METHODS: The course consists of fifteen two-hour lectures (30 hours total). To reinforce the material, participants will receive weekly home assignments providing hands-on experience. COURSE STRUCTURE: 1. Introduction to quantum dynamics 2. Unitary evolution operator and Hamiltonian 3. Schrieffer–Wolff transformation: effective Hamiltonians and perturbation theory 4. Disentanglement theorem: time-ordered exp and time-dependent Hamiltonian 5. Magnus expansion 6. Adiabatic theorem 7. Green function methods and cluster expansion Chapters: 0:00 Recap 10:45 Direct rotation 1:04:04 Procedure for generating perturbation series 1:46:27 Diagrammatology 2:01:00 Radius of convergence