Review of a Simplified Approach to study the Bose gas at all densities
Abstract
In this paper, 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 oneparticle equations, which capture some nontrivial physical properties of the Bose gas at both low 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 meanfield estimate for the energy at high densities. We will also discuss a phase that appears at intermediate densities with liquidlike 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 arXiv:
 arXiv:2202.07637
 Bibcode:
 2022arXiv220207637J
 Keywords:

 Mathematical Physics;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics