Gauge Transformation of the Gross-Pitaevskii Equation Coupled by Time- Dependent Potential - Prayitno, T. B. (Jurnal Spektra, 2013)
We have presented some appropriate gauge transformations for the three-dimensional Gross-Pitaevskii equation coupled by time-dependent potential. The purpose of this paper is to determine both explicitly and implicitly all the functions to keep the present Gross-Pitaevskii equation by initially introducing the modified Gross-Pitaevskii and then imposing the condition of transformations which is adopted from the gauge transformation of classical electrodynamics. This work can be done since the present Gross-Pitaevskii equation can be manipulated to be gauge invariance after the wave function has been transformed through the local phase transformation. In this case, we only discuss its mathematical aspects and ignore the physical interpretation to open all the possibilities. However we have still imposed that all the lengths of vectors must be positive real to agree with the mathematical concept and found that only two cases can be explored since it is not possible to obtain the appropriate transformations, except we set the potential vector-like vectorto be zero and the phase to be an arbitrary function of time.Keywords: gauge transformations, Gross-Pitaevskii equation, gain-loss term.