the range $1-2$, although all authors agree on the functional form.

2.1. Candidates for BEC
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There are several candidates for BEC. A first attempt to experimentally observe BEC was made with superfluidity. When $^{4}$He is cooled to a critical temperature of 2.17K, the liquid density drops, and fractions of the liquid become superfluid. The strong interaction of $^{4}$He in liquid form prevents perfect condensation. The formation of Cooper pairs of electrons, which act like bosons, is also evidence of the condensation effect, which produces superconductivity [@1; @15]. However, in these systems, a macroscopic wave function provides only a phenomenological description of the superfluid state.

By contrast, the macroscopic wave function of pure condensates is directly connected with the microscopic degrees of freedom, providing a complete and quantitative description of both static and dynamic phenomena. This description should cover systems showing a true BEC phase. Some systems were cited, such as excitons-polaritons, which are light-mass quasi-particles usually produced by optical excitations in semiconductors, and photons confined in a cavity [@1; @11; @15; @16; @17]. However, excitons have a very short lifetime and the photons are absorbed by the walls. Because the BEC requires a thermalization time to condense in which 