Existence of Long-Range Order for Trapped Interacting Bosons

TL;DR

This paper derives an inequality linking long-range order in trapped Bose condensates to physical parameters, providing an experimentally testable upper bound on condensate size in one-dimensional systems.

Contribution

It introduces a new inequality that relates condensate fraction, trap curvature, and particle number, offering a novel theoretical tool for analyzing trapped Bose gases.

Findings

Derived an inequality for long-range order in Bose condensates.

Provided an explicit upper bound for condensate size in 1D traps.

Suggested experimental tests for the inequality in current setups.

Abstract

We derive an inequality governing ``long range'' order for a localized Bose-condensed state, relating the condensate fraction at a given temperature with effective curvature radius of the condensate and total particle number. For the specific example of a one-dimensional, harmonically trapped dilute Bose condensate, it is shown that the inequality gives an explicit upper bound for the Thomas-Fermi condensate size which may be tested in current experiments.