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We analyze the phase transition associated with the U(1) symmetry breaking of the complex Klein-Gordon (KG) equation with a Mexican-hat scalar field potential up to one loop in perturbations immersed in a thermal bath. We show that the KG equation reduces to a Gross-Pitaevskii like-equation (GP), which also contains the entire information of the phase transition. Indeed, the thermal bath contributions, together with the corresponding U(1) local symmetry, allow us to interpret the resulting GP equation as a charged and finite temperature version of the system. Finally, we obtain the hydrodynamics and consequently, the corresponding thermodynamics, and show that breakdown of the U(1) local symmetry of the KG field into the new version of the GP equation corresponds, under certain circumstances, to a phase transition of the gas into a condensate, superfluid, and/or superconductor. [ABSTRACT FROM AUTHOR]

We analyze the the remarkable analogy between the classical Klein-Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross-Pitaevskii equation for a Bose-Einstein condensate trapped by an external potential. We stress here that the solution associated with the Klein-Gordon equation (KG) in a flat space time has the same mathematical structure, under certain circumstances, to those obtained for the Gross-Pitaevskii equation, that is, a static soliton solution. Additionally, Thomas-Fermi approximation is applied to the 3-dimensional version of this equation, in order to calculate some thermodynamical properties of the system in curved a space-time back ground. Finally, we stress the fact that a gravitational background provides, in some cases, a kind of confining potential for the scalar field, allowing us to remarks even more the possible connection between scalar fields and the phenomenon of Bose-Einstein condensation. [ABSTRACT FROM AUTHOR]

The experimental requirements that could lead to the detection of the so-called deformed dispersion relations, in the context of Sagnac interferometry, are obtained. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]