Non-perturbative 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 Monte-Carlo simulations. In this talk, I will first give an overview of this Simplified approach, and will discuss evidence for non-perturbative behavior in the intermediate density regime obtained using this tool.

Slides

PDF:

• Jauslin_Princeton_2023.pdf

• tarball: 23princeton-1.0.tar.gz
• git repository: 23princeton-git (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 659-684, 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 5322-5360, 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 609-635)
  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