Im Wintersemester 2024/25 hält Dr. Sascha Lill von der Università degli Studi di Milano die Gastvorlesung 'Vielteilchentheorie' (Original: 'Many-Body Quantum Mechanics') an der UPB. Die Vorlesungen finden im Blockformat im Oktober und Dezember 2024 statt. Die Lehrveranstaltung richtet sich an Studierende im Master Mathematik. Studierende im Bachelor sowie anderer Fächer, insbesondere Physik und Informatik, sind herzlich willkommen - ebenso Promovierende.
Beschreibung der Vorlesungsinhalte:
This course provides an introduction into the essential mathematical tools needed to study many-body quantum systems.
We start with recalling some elementary properties of operators on Hilbert spaces, which allow us to define dynamics of a quantum system, as well as its ground state and thermal equilibrium states. To apply these notions to systems with many particles, we introduce tools including symmetric and antisymmetric tensor products (for bosons or fermions), Fock spaces, creation and annihilation operators and the second quantization of a one-body operator. If time permits, we will also cover Bogoliubov transformations, which are fundamental in quantum optics, as well as in the celebrated Bogoliubov theory and BCS theory.