Fluctuation correction to the ground state energy density of a dilute Bose gas in the functional Schr\"{o}dinger picture

TL;DR

This paper develops a variational approach using a shifted Gaussian wavefunctional in the functional Schrödinger picture to compute fluctuation corrections to the ground state energy density of a dilute Bose gas, including higher order effects.

Contribution

It introduces a novel shifted Gaussian trial wavefunctional method to calculate fluctuation corrections in the ground state energy of a dilute Bose gas.

Findings

Calculated higher order fluctuation correction to the ground state energy

Compared the correction with quantum scattering contributions

Demonstrated the effectiveness of the variational approach in this context

Abstract

A dilute Bose gas system is studied using the functional Schr\"{o}dinger picture theory. The ground state properties are obtained by solving the infinite dimensional Schr\"{o}dinger equation variationally. It is shown that a shifted Gaussian trial wavefunctional enables us to calculate a higher order correction, which corresponds to the fluctuation contribution from the condensate. The obtained term is compared with the quantum correction arising from the low energy $3 \to 3$ scattering.