Mathematics of Bose-Einstein Condensation
Informacje ogólne
Kod przedmiotu: | 1100-MBEC |
Kod Erasmus / ISCED: | (brak danych) / (brak danych) |
Nazwa przedmiotu: | Mathematics of Bose-Einstein Condensation |
Jednostka: | Wydział Fizyki |
Grupy: |
Fizyka, II stopień; przedmioty z listy "Wybrane zagadnienia fizyki współczesnej" Physics (Studies in English), 2nd cycle; courses from list "Topics in Contemporary Physics" Physics (Studies in English); 2nd cycle Przedmioty do wyboru dla doktorantów; |
Punkty ECTS i inne: |
(brak)
|
Język prowadzenia: | angielski |
Założenia (opisowo): | Knowledge of analysis, functional analysis and operator theory are welcome but not necessary. |
Tryb prowadzenia: | w sali |
Skrócony opis: |
The aim of the course is to provide an up-to-date, self-contained introduction into the mathematical analysis of quantum many-boson systems. |
Pełny opis: |
The goal of the course is to provide an up-to-date, self-contained introduction into the mathematical analysis of quantum many-boson systems. The main goal is to discuss the concept of Bose-Einstein Condensation and related topics (such as superfluidity) from a rigorous point of view. We plan to cover the following topics: (1) Principles of quantum statistical mechanics. (2) The concept of Bose-Einstein Condensation. (3) Scaling limits: from Hartree to Gross-Pitaevskii. (4) Bogoliubov theory and superfluidity. (5) Quantum dynamics: the nonlinear Schrodinger equation. Our aim is to make the lecture accessible to both physicists and mathematicians. Research projects will be proposed during the course. |
Literatura: |
E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason: The Mathematics the of Bose gas and its condensation, Birkhäuser; J.P. Solovej, Many Body Quantum Mechanics Robert Seiringer, "Hot topics in cold gases", Japan. J. Math. 8, 185-232 (2013) M. Lewin, P.T. Nam, S. Serfaty, J.P. Solovej, Bogoliubov spectrum of interacting Bose gasges, Comm. Pure App. Math. 68 (3), 413–471 (2015) |
Efekty uczenia się: |
Knowledge: Knowledge of the mathematical basics of Bose-Einstein condensation theory. Skills: Derivation and justification of major effective theories. Attitude: Precision of thought and pursuit of a deeper understanding of theoretical formalisms used in physics. |
Metody i kryteria oceniania: |
Oral exam. |
Praktyki zawodowe: |
Do not apply |
Właścicielem praw autorskich jest Uniwersytet Warszawski, Wydział Fizyki.