hal-03368550
https://cnrs.hal.science/hal-03368550
https://cnrs.hal.science/hal-03368550/document
https://cnrs.hal.science/hal-03368550/file/PhysRevA.103.053309.pdf
arxiv:2011.10869
doi:10.1103/PhysRevA.103.053309
[UGA] HAL Grenoble Alpes
[CNRS] CNRS - Centre national de la recherche scientifique
[LPMMC] Laboratoire de Physique et Modélisation des Milieux Condensés
[UGA-EPE] Université Grenoble Alpes [2020-*]
Simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy
Carlen, Eric A.
Holzmann, Markus
Jauslin, Ian
Lieb, Elliott H.
[PHYS.COND] Physics [physics]/Condensed Matter [cond-mat]
ART
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.
2021
2021-10-06
en
Physical Review A : Atomic, molecular, and optical physics
American Physical Society