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

J. Gamboa

Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago, Chile

E-mail Address: jgamboa55@gmail.com

Corresponding author.

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F. Méndez

Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago, Chile

E-mail Address: fernando.mendez.f@gmail.com

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Justo López-Sarrión

Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí Franquès 1, 08028 Barcelona, Spain

E-mail Address: justo.lopezsarrion@ub.edu

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https://doi.org/10.1142/S0217732322502376Cited by:1 (Source: Crossref)

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 $(𝜃)$ and, at second order in $𝜃$ , our procedure yields to the standard dipole–dipole interaction with $𝜃^{2}$ playing the role of the strength interaction parameter. The generalized Gross–Pitaevskii equation containing nonlocal dipolar contributions is found. For $^{52} Cr$ isotopes $𝜃 = C_{d d} / 4 π$ becomes $\sim$ $1 0^{- 11} cm$ and, thus for this value of $𝜃$ one cannot distinguish interactions coming from non-commutativity or those of dynamical origin.

Keywords:

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