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'. Synopsis (Kurzbeschreibung): 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 |
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