Mathematics of Bose-Einstein Condensation

Knowledge of analysis, functional analysis and operator theory are welcome but not necessary.

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The aim of the course is to provide an up-to-date, self-contained introduction into the mathematical analysis of quantum many-boson systems.

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.

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)

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.

Oral exam.

Do not apply