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

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 $θ$. 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.