A simple equation to study interacting Bose gasses
Texas A&M, College Station, Texas, USA
May 15, 2020
In this talk, I will discuss a partial differential equation introduced by Lieb in 1963 in the context of studying interacting Bose gasses. I will first discuss how this equation can be used to accurately compute physically relevant quantities related to the Bose gas, such as the ground state energy and condensate fraction. I will then present a construction of the solutions to the equation, and discuss some of their properties.
Slides
PDF:
LaTeX source:
 tarball: 20tamu1.0.tar.gz
 git repository: 20tamugit (the git repository contains detailed information about the changes in the slides as well as the source code for all previous versions).
References
This presentation is based on

[CJL19]: Analysis of a simple equation for the ground state energy of the Bose gas
Eric Carlen, Ian Jauslin, Elliott H. Lieb, 2019
(published in Pure and Applied Analysis, volume 2, issue 3, pages 659684)
pdf, source 
[CJLL20]: On the convolution inequality f>f*f
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, Michael Loss, 2020
(published in International Mathematics Research Notices, Volume 2021, Issue 24, pages 1860418612, 2021)
pdf, source