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 non-trivial.

Slides

PDF:

• Jauslin_Rutgers_2023.pdf

• tarball: 23rutgers-1.0.tar.gz
• git repository: 23rutgers-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