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Bose-Einstein condensates in a homogeneous gravitational field

The behavior of a Bose--Einstein condensate in a homogeneous gravitational field is analyzed. We consider two different trapping potentials. Firstly, the gas is inside a finite container. The effects of the finiteness of the height of the container in connection with the presence of a homogeneous gravitational field are mathematically analyzed and the resulting energy eigenvalues are deduced and used to obtain the corresponding partition function and the ensuing thermodynamical properties. Secondly, the trapping potential is an anisotropic harmonic oscillator and the effects of the gravitational field and of the zero--point energy on the condensation temperature are also considered. These results are employed in order to put forward an experiment which could test the so called Einstein Equivalence Principle.