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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Hydrodynamic Version of the Equation of Motion of a Charged Complex Scalar Field
verfasst von : Mario A. Rodríguez-Meza, Tonatiuh Matos
Erschienen in: Computational and Experimental Fluid Mechanics with Applications to Physics, Engineering and the Environment
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Abstract
In this chapter we derive the equation for a charged complex scalar field in its hydrodynamic form. This is done by re-writing the Klein-Gordon (KG) equation for the complex scalar field as a new Gross-Pitaevskii (GP)-like equation. In particular, we use as the potential of the scalar field the Mexican-hat potential, and assume that the field is in a thermal bath with a one loop contribution. We interpret the new GP equation as a finite temperature generalization of the GP equation for a charged field. From its hydrodynamic form, we derive the corresponding thermodynamics and obtain a generalized first law for a charged Bose-Einstein Condensate (BEC).