Nonperturbative behavior of interacting Bosons at intermediate densities
Princeton, New Jersey, USA
April 18, 2023
Much attention has been given to systems of interacting Bosons in the dilute regime, where powerful theoretical tools such as Bogolyubov theory give detailed and accurate predictions. In this talk, I will discuss a different approach to studying the ground state of Boson systems, which Carlen, Lieb and I have recently found to be accurate at all densities. In particular, it allows us to probe the system in the intermediate density regime, which had, until now, only been accessible to costly MonteCarlo simulations. In this talk, I will first give an overview of this Simplified approach, and will discuss evidence for nonperturbative behavior in the intermediate density regime obtained using this tool.
Slides
PDF:
LaTeX source:
 tarball: 23princeton1.0.tar.gz
 git repository: 23princetongit (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 
[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
pdf, source 
[Ja23b]: Evidence of a liquid phase in interacting Bosons at intermediate densities
Ian Jauslin, 2023
pdf, source