Ian Jauslin

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, two-point 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 many-body 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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Numerical computations

The numerical computations in this paper were carried out using simplesolv v0.3, which is available on this website.

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