Vorlesung (Block-kurs): De Finetti theorems, mean-field limits and Bose-Einstein condensation (N. Rougerie) (SoSe 2015)
News (June 18th): Second version of the lecture notes is here (and at arXiv:1506.05263).
News (June 18th): The students having handed in homework can pick up their 'Schein' at the secretary's office
News (April 21th): You can find the slides from the first lecture here.
News (April 10th): First version of the lecture notes is here.
Lecturer: Nicolas Rougerie (CNRS / Université Grenoble-Alpes).
Time, room: This is a 'Block-kurs' consisting of 9 lectures each of two hours. It is an English version of N. Rougerie's 'Cours Peccot' at Collège de France. It takes place in B 134 at the following times:
20 - 24 April 2015 (Mo-Fr) 18-20Uhr & 27 - 30 April 2015 (Mo-Thu) 18-20Uhr.
Exercises (Übungen): There will be a number of homeworks for students wishing to acquire a 'Schein'.
The course will adress the mean-field approximation for the equilibrium states of N-body systems in classical and quantum statistical mechanics. The main goal is a rigorous derivation from first principles of effective models that are usually based on statistical independence assumptions. A general strategy to achieve this will be discussed in details. The main tools are structure theorems "à la de Finetti" which describe the possible large-N limits of the admissible states of statistical mechanics. The main application we have in mind is the Bose-Einstein condensation phenomenon, which takes place in cold dilute Bose gases. Accordingly, the main emphasis of the course will be on the justification of the mean-field approximation for the ground state of large bosonic systems. We shall discuss topics such as the concentration-compactness principle, localization methods in Fock space, the structure of bosonic density matrices, the Hartree and Gross-Pitaevskii functionals etc.
Audience (Hörerkreis): Master students of Mathematics and Physics, TMP-Master.
Credits: 2 ECTS.
Exam (Prüfung): There will be a number of homeworks for students wishing to acquire a 'Schein'. The exact modus will be discussed by Prof. Rougerie in the lectures.
Prerequisites: A basic knowledge of Mathematical Quantum Mechanics (corresponding to the course 'Mathematical Quantum Mechanics 1' (MQM1)) is an advantage.
Language (Sprache): English.
Literature: There will be lecture notes. These will be updated regularly.
First version of the lecture notes is here (version 1: March 2015).
Second version of the lecture notes is here (version 2: May 2015); see also arXiv:1506.05263.
(A version (in French) of N. Rougerie's notes for the 'Cours Peccot' at Collège de France can be found here.)
Letzte Änderung: 26 June 2015 (no more updates).
Thomas Østergaard Sørensen