Review of a simplified approach to study the Bose gas at all densities
type: Item
instance of: scholarly article
title: Review of a simplified approach to study the Bose gas at all densities
author: Ian Jauslin
publication date: 2022-08-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/2202.07637
full work available at URL: https://ems.press/books/standalone/235/4512
review text: Summary: In this chapter, we will review the results obtained thus far by Eric A. Carlen, Elliott H. Lieb, and me on a Simplified Approach to the Bose gas. The Simplified Approach yields a family of effective one-particle equations, which capture some non-trivial physical properties of the Bose gas at bothlow and high densities, and even some of the behavior at intermediate densities. In particular, the Simplified Approach reproduces Bogolyubov's estimates for the ground state energy and condensate fraction at low density, as well as the mean-field estimate for the energy at high densities. We will also discuss a phase that appears at intermediate densities with liquid-like properties. The simplest of the effective equations in the Simplified Approach can be studied analytically, and we will review several results about it; the others are so far only amenable to numerical analysis, and we will discuss several numerical results. We will start by reviewing some results and conjectures on the Bose gas and then introduce the Simplified Approach and its derivation from the Bose gas. We will then discuss the predictions of the Simplified Approach and compare these to results and conjectures about the Bose gas. Finally, we will discuss a few open problems about the Simplified Approach. For the entire collection see [Zbl 1491.46002].
Mathematics Subject Classification ID: 82-XX
zbMATH DE Number: 7571349
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7571349