Non-perturbative behavior of interacting Bosons at intermediate densities

Condensed Matter Theory Fall 2023 Symposium, Rutgers University, New Jersey, USA

December 19, 2023

In this talk, I will discuss the behavior of systems of many Bosons interacting via a repulsive, positive-type 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 many-Boson systems at all densities.

Slides

PDF:

• Jauslin_SMM125_2023.pdf

• tarball: 23smm125-1.0.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 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


• [Ja23c]: Bose-Einstein condensation and the Simplified Approach to interacting Bosons
  Ian Jauslin, 2023
  pdf, source