Effects of spatial noncommutativity on energy spectrum of a trapped Bose-Einstein condensate

TL;DR

This paper investigates how spatial noncommutativity influences the energy spectrum of a trapped Bose-Einstein condensate, revealing a reduction in ground-state energy and a potential signal of noncommutative space effects.

Contribution

It provides an analytic expression for the energy spectrum of a Bose-Einstein condensate in noncommutative space, highlighting the impact of noncommutativity on ground-state energy levels.

Findings

Ground-state energy is reduced due to noncommutativity.

A gap between noncommutative and commutative space energies is identified.

The gap depends on the noncommutativity parameter θ.

Abstract

In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose-Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutativity on energy spectrum of the condensate. It indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter $\theta$. The appeared gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.