Bose–Einstein condensation theory for any integer spin: Approach based in noncommutative quantum mechanics

Abstract

A Bose–Einstein condensation theory for any integer spin using noncommutative quantum mechanics methods is considered. The effective potential is derived as a multipolar expansion in the non-commutativity parameter [Formula: see text] and, at second order in [Formula: see text], our procedure yields to the standard dipole–dipole interaction with [Formula: see text] playing the role of the strength interaction parameter. The generalized Gross–Pitaevskii equation containing nonlocal dipolar contributions is found. For [Formula: see text] isotopes [Formula: see text] becomes [Formula: see text][Formula: see text][Formula: see text] and, thus for this value of [Formula: see text] one cannot distinguish interactions coming from non-commutativity or those of dynamical origin.