Mathematisches Seminar: Bogoliubov spectrum of interacting Bose gases (WS 2013/14)

Time, room: Tuesday 8-10 in B 252

First meeting: Tuesday October 15th, 2014 in B 252 (Intro, motivation, topics).

Vorträge können auch auf Deutsch gehalten werden!

If interested, please sign up via email ( ) until 14.10.2013.

Synopsis: We will read (and present) the paper mentioned below.

Its abstract:

"We study the large-N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next order, predicted by Bogoliubov's theory. We show the convergence of the lower eigenvalues and eigenfunctions towards that of the Bogoliubov Hamiltonian (up to a convenient unitary transform). We also prove the convergence of the free energy when the system is sufficiently trapped. Our results are valid in an abstract setting, our main assumptions being that the Hartree ground state is unique and non-degenerate, and that there is complete Bose-Einstein condensation on this state. Using our method we then treat two applications: atoms with "bosonic" electrons on one hand, and trapped 2D and 3D Coulomb gases on the other hand."

Audience: Master students of Mathematics and Physics, TMP-Master.

Prerequisites: MQM2 (SoSe2013) or equivalent knowledge (i.e., J. P. Solovej, Many Body Quantum Mechanics, August 30, 2009).

Language: The speakers can choose between English and German.

Literature: [LNSS] M. Lewin, P. T. Nam, S. Serfaty, and J. P. Solovej, Bogoliubov spectrum of interacting Bose gases, arXiv:1211.2778v3, 2013. (Final version to appear in Comm. Pure Appl. Math., 2013).

Office hours: Thursday 10:15-11:00 (Room B 408) or by appointment via email.

Programme (Talks start at 08:30):

Datum Speaker           Title             Remarks        
15.10.2013     Thomas Sørensen     Intro, motivation, topics.
5.11.2013    Thomas Sørensen     Main results I. pp. 2-16.
12.11.2013     Thomas Sørensen     Main results II. pp. 2-16.
19.11.2013     Oliver Lindblad Petersen     Bosonic atoms. pp. 16-20.
26.11.2013     Johannes Alt     Trapped Coulomb gases. pp. 20-24.
03.12.2013     Dominik Schröder     Logarithmic Lieb-Oxford inequality. pp. 46-49.
10.12.2013     Dominik Schröder     Operators on Fock space. pp. 24-28.
17.12.2013     Oliver Lindblad Petersen    Proof of Proposition 15. pp. 28-32.
07.01.2014     Anton Samojlow    Localization in Fock space. pp. 32-33 & 46.
14.01.2014     Anton Samojlow    Proof of Theorem 2. pp. 33-37.
21.01.2014     Johannes Alt     Bogoliubov Hamiltonians. pp. 40-45.

Wie halte ich einen Seminarvortrag? von Prof. Dr. Manfred Lehn, Johannes Gutenberg-Universitätt Mainz.


Letzte Änderung: 21. January 2014 (no more updates).

Thomas Østergaard Sørensen

Curriculum Vitae