Polymer quantization in the Bogoliubov's regime for a homogeneous one-dimensional Bose-Einstein condensate

TL;DR

This paper investigates how polymer quantization affects the ground state and sound velocity of a homogeneous one-dimensional Bose-Einstein condensate, highlighting potential observable corrections in dense, small scattering length systems.

Contribution

It introduces a novel analysis of polymer quantization effects on BEC ground state energy and sound speed within the Bogoliubov regime, emphasizing the system's sensitivity to space discreteness.

Findings

Polymer corrections are more significant in dense systems with small scattering lengths.

Finite size effects constrain the magnitude of polymer quantization corrections.

The ground state energy and sound velocity are affected by the polymer length scale.

Abstract

In the present report we analyze the eventual modifications caused by the polymer quantization upon the ground state of a homogeneous one-dimensional Bose-Einstein condensate. We obtain the ground state energy of the corresponding N-body system and, consequently, the corresponding speed of sound, allowing us to explore the sensitivity of the system to corrections caused by the polymer quantization. The corrections arising from the polymer quantization can be improved for dense systems together with small values of the corresponding one-dimensional scattering length. However, these corrections remain constrained due to finite size effects of the system. The contributions of the polymer length scale to the properties of the ground state energy of the system allow us to explore, as a first approximation and when the Bogoliubov's formalism is valid, the sensitivity of this many-body system to traces caused by the discreteness of space suggested by the polymer quantization.