Nonperturbative behavior of interacting Bosons at intermediate densities
Condensed Matter Theory Fall 2023 Symposium, Rutgers University, New Jersey, USA
September 29, 2023
In this talk, I will discuss the behavior of systems of many Bosons interacting via a repulsive, positivetype potential at intermediate densities. The interacting Bose gas has been studied extensively in the low and high density regimes, in which interactions do not play a physically significant role, and the system behaves similarly to (effectively) ideal quantum gases. Instead, I will focus on the intermediate density regime, and report evidence that the system enters a strongly correlated phase where its behavior is markedly different from that of the ideal quantum gas. To do so, I will use the Simplified approach to the Bose gas, which was introduced by Lieb in 1963 and was recently found to provide very accurate predictions for manyBoson systems at all densities.
Slides
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 tarball: 23cmt1.0.tar.gz
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 
[Ja23c]: BoseEinstein condensation and the Simplified Approach to interacting Bosons
Ian Jauslin, 2023
pdf, source