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
Abstract
In 1963, a Simple Approach was developed to study the ground state energy of an interacting Bose gas. It consists in the derivation of an Equation, which is not based on perturbation theory, and which gives the exact expansion of the energy at low densities. This Equation is expressed directly in the thermodynamic limit, and only involves functions of 3 variables, rather than 3N. Here, we revisit this approach, and show that the Equation yields accurate predictions for various observables for all densities. Specifically, in addition to the ground state energy, we have shown that the Simple Approach gives predictions for the condensate fraction, twopoint correlation function, and momentum distribution. We have carried out a variety of tests by comparing the predictions of the Equation with Quantum Monte Carlo calculations, and have found remarkable agreement. We thus show that the Simple Approach provides a new theoretical tool to understand the behavior of the manybody Bose gas, not only in the small and large density ranges, which have been studied before, but also in the range of intermediate density, for which little is known.
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 git repository: 20chjlgit (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
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 arXiv preprint: arXiv:2011.10869.
 This article was peer reviewed by and published in: Physical Review A, Volume 103, Number 053309, 2021
Numerical computations
The numerical computations in this paper were carried out using simplesolv, which is available on this website.
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Talks
This work has been presented at the following conferences:

[Ga22]: An effective equation to study Bose gases at all densities
Advances in Classical, Quantum and Statistical Mechanics  A celebration of the work and contributions of Giovanni Gallavotti  On the occasion of his 80th birthday, Rome, Italy, May 13 2022
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[Mi22]: An effective equation to study Bose gases at all densities
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[Tu22]: An effective equation to study Bose gases at all densities
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[LMU21]: An effective equation to study Bose gases at all densities
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[Ye21]: An effective equation to study Bose gases at all densities
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[Ja21]: An effective equation to study Bose gases at all densities
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[Pe21]: An effective equation to study Bose gases at all densities
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[MC21]: Many interacting quantum particles: open problems, and a new point of view on an old problem
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[Cop21]: An effective equation to study Bose gasses at all densities
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[TAMU20b]: A new approach to the Mathematics of the Bose gas
Texas A&M, College Station, Texas, USA, Nov 30 2020
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