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Evidence of a liquid phase in interacting Bosons at intermediate densities

Ian Jauslin

2023

Abstract

In this paper, we present evidence for a liquid-like phase in systems of many interacting Bosons 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 the ideal quantum gas. Instead, we will turn our attention to 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, we use the Simplified approach to the Bose gas, which was introduced by Lieb in 1963 and recently found to provide very accurate predictions for many-Boson systems at all densities. Using this tool, we will compute predictions for the radial distribution function, structure factor, condensate fraction and momentum distribution, and show that they are consistent with liquid-type behavior.

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• Jauslin_2023b.pdf

LaTeX source:

• tarball: 23j_b-0.0.1.tar.gz
• git repository: 23j_b-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).

simplesolv

The graphs in this paper were obtained using simplesolv v0.4.

Other releases

• arXiv preprint: arXiv:2302.13449.

Related articles

• [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)
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• [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)
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• [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)
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• [Ja23]: The Simplified approach to the Bose gas without translation invariance
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Talks

This work has been presented at the following conferences:

• [Da23]: Non-perturbative behavior of interacting Bosons at intermediate densities
  UC Davis, California, USA, May 30 2023
  pdf


• [Pr23]: Non-perturbative behavior of interacting Bosons at intermediate densities
  Princeton, New Jersey, USA, Apr 18 2023
  pdf


• [SISSA23]: Interacting Bosons at intermediate densities
  SISSA, Trieste, Italy, Mar 16 2023
  pdf


• [Ru23]: Interacting Bosons at intermediate densities
  Rutgers University, New Jersey, USA, Mar 09 2023
  pdf