Interacting Bosons at intermediate densities
Rutgers University, New Jersey, USA
March 9, 2023
Carlen, Lieb and I have recently revived an old approach to the Bose gas, called the Simplified Approach, and found that it gives very accurate predictions at all densities, at least for a certain class of potentials. Using this method, we have investigated the intermediate density regime, whose analysis had previously been too difficult due to the perturbative nature of previous theoretical tools. In this talk, I will first review the Simplified Approach, and then present evidence for the fact that the behavior of Boson systems in the intermediate density regime is nontrivial.
Slides
PDF:
LaTeX source:
 tarball: 23rutgers1.0.tar.gz
 git repository: 23rutgersgit (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, 2020)
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, 2021)
pdf, source 
[Ja22]: Review of a Simplified Approach to study the Bose gas at all densities
Ian Jauslin, 2022
(published in The Physics and Mathematics of Elliott Lieb, The 90th anniversary Volume 1, pages 609635)
pdf, source 
[Ja23]: The Simplified approach to the Bose gas without translation invariance
Ian Jauslin, 2023
(published in Journal of Statistical Physics, Volume 191, number 88, 2024)
pdf, source 
[Ja23b]: Evidence of a liquid phase in interacting Bosons at intermediate densities
Ian Jauslin, 2023
pdf, source