An effective theory for interacting Bose gases

(Reading seminar summer 2021)

Phan Thành Nam - Uni2work

General Information

Goal: In this seminar we will study a simplified equation for interacting Bose gases, which was proposed by E.H. Lieb in 1963 and has gained renewed interest from many researchers. The model is based on a non perturbative approximation for the correlation function associated to the ground state, leading to a non local elliptic equation for the density. Despite of its simplicity, the equation predicts correctly many important properties of the many-body quantum systems at all densities.

Audience : Bachelor and Master students of Mathematics and Physics.

Time and place: The meetings will take place on Zoom every Wednesday, 14:15-15:45, starting from April 21.
Zoom link (Meeting ID: 948 1239 6687, Passcode: 554082)

References:

• Elliott H. Lieb, Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas, Physical Review 130, p. 2518-2528 (1963).
• Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, Michael Loss, On the convolution inequality f>f*f, arXiv:2002.04184
• Eric Carlen, Ian Jauslin, and Elliott H. Lieb, Analysis of a simple equation for the ground state energy of the Bose gas, Pure and Applied Analysis, Vol. 2, 659–684 (2020).
• Elliott H. Lieb and Jakob Yngvason, Ground State Energy of the Low Density Bose Gas. Phys. Rev. Lett. 80, 2504 (1998).
• Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, Analysis of a simple equation for the ground state of the Bose gas II: Monotonicity, Convexity and Condensate Fraction, arXiv:2010.13882.

Schedule:

21.04.2021. Overview of macroscopic properties of Bose gases. Slides.

28.04.2021. Introduction to the effective model. This will be presented by Ian Jauslin in this seminar.

05.05.2021. Distribution of materials. Plan.

19.05.2021. Lena Heidenreich. Slides

26.05.2021. Markus Wiener. Slides

02.06.2021. Tilman Baus. Slides

09.06.2021. Jakob Oldenburg. Slides

16.06.2021. Jinyeop Lee. Slides-Notes

23.06.2021. Chun Yin Lam. Slides

30.06.2021. Charlotte Dietze. Notes