Department Mathematik
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Bose gases at positive temperature

(Reading seminar Summer 2026)

Phan Thành Nam, Cornelia Vogel, Moodle (ID: 46605, pass: BosGas2026).

General Information

Description: We will discuss macroscopic behaviors of interacting Bose gases at low temperature, focusing on the free energy, the Bose-Einstein condensation and related phenomena.

Audience : Bachelor and Master students of Mathematics.

Credits: 3 ECTS.

Language: English.

Time and place: Tuesday 14:15-16:00 (B045)

References:
  • A. Einstein, Quantentheorie des einatomigen idealen Gases, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1925) 1: 3 (in German). [1]
  • N. N. Bogoliubov, On the theory of superfluidity, J. Phys. (USSR), 11 (1947), p. 23. [2]
  • T. D. Lee and C. N. Yang, Low-Temperature Behavior of a Dilute Bose System of Hard Spheres. I. Equilibrium Properties, Phy. Rev. 112 (5) (1958), pp. 1419–1429. [3]
  • E. H. Lieb, R. Seiringer, J.P. Solovej and J. Yngvason, Mathematics of Bose gas and its condensation, Oberwolfach Seminar Series, Vol. 34, Birkhaeuser (2005). [4]
  • R. Seiringer, The excitation spectrum for weakly interacting bosons, Commun. Math. Phys. 306 (2011), pp. 565–578. [5]
  • R. Seiringer, Free Energy of a Dilute Bose Gas: Lower Bound, Commun. Math. Phys. 279 (2008), p. 595–636. [6]
  • G. Basti, C. Boccato, S. Cenatiempo and A. Deuchert, A new upper bound on the specific free energy of dilute Bose gases. arXiv:2507.20877 2025), 83 pages. [7]
  • A. Deuchert, P.T. Nam and M. Napiórkowski, The Gibbs state of the mean-field Bose gas. arXiv:2501.19396 (2025), 102 pages. [8]

Schedule:

21.4.2026. Introduction and distribution of the reading material.

28.4.2026. Cornelia Vogel. The free Bose gas. [1,4]

Bogoliubov theory for the interacting Bose gas. [2,3,8]

The mean-field Bose gas at low temperature. [5]

The free energy of the interacting Bose gas: lower bound. [6]

The free energy of the interacting Bose gas: upper bound. [7]