Many interacting quantum particles: open problems, and a new point of view on an old problem
Mathematical Conversations, Institute for Advanced Study, Princeton, NJ, USA
March 10, 2021
The main object of interest in this talk will be a system of many particles, modeled using the prescriptions of quantum mechanics. A significant challenge to studying such systems is that particles interact with each other, via weak or strong, attractive or repulsive forces, which induce correlations, and make it so that, to understand the properties of the system, one must understand the behavior of all particles at once. In this talk, I will consider one of the simplest interacting quantum systems, called the "Bose gas", and I will review what is known, and discuss a collection of open questions. Finally, I will discuss an approach to this model, which may seem odd at first glance, but which seems to be very successful to understand the properties of the interacting Bose gas in a way that is conceptually and computationally simple.
Slides
PDF:
LaTeX source:
 tarball: 21mc1.0.tar.gz
 git repository: 21mcgit (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 
[CJL20]: Analysis of a simple equation for the ground state of the Bose gas II: Monotonicity, Convexity and Condensate Fraction
Eric A. Carlen, Ian Jauslin, Elliott H. Lieb, 2020
(published in SIAM Journal on Mathematical Analysis, Volume 53, Number 5, pages 53225360, 2021)
pdf, source 
[CHJL20]: A simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy
Eric A. Carlen, Markus Holzmann, Ian Jauslin, Elliott H. Lieb, 2020
(published in Physical Review A, volume 103, number 053309)
pdf, source