(in Polish) Mathematics of Bose-Einstein Condensation

General data

Course ID:	1100-MBEC
Erasmus code / ISCED:	(unknown) / (unknown)
Course title:	(unknown)
Name in Polish:	Mathematics of Bose-Einstein Condensation
Organizational unit:	Faculty of Physics
Course groups:	(in Polish) Physics (Studies in English), 2nd cycle; courses from list "Topics in Contemporary Physics" (in Polish) Physics (Studies in English); 2nd cycle (in Polish) Przedmioty do wyboru dla doktorantów; Physics (2nd cycle); courses from list "Selected Problems of Modern Physics"
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Prerequisites (description):	(in Polish) Knowledge of analysis, functional analysis and operator theory are welcome but not necessary.
Mode:	Classroom
Short description:	(in Polish) The aim of the course is to provide an up-to-date, self-contained introduction into the mathematical analysis of quantum many-boson systems.
Full description:	(in Polish) 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.
Bibliography:	(in Polish) 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)
Learning outcomes:	(in Polish) 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.
Assessment methods and assessment criteria:	(in Polish) Oral exam.
Practical placement:	(in Polish) Do not apply

This course is not currently offered.

Course descriptions are protected by copyright.
Copyright by University of Warsaw.