The equation of state of one-dimensional Gross-Pitaevskii equation

Abstract

We have constructed the equation of state of one-dimensional Gross-Pitaevskii equation by benefiting from the formulation of a single macroscopic particle partition function and then modeling N undistinguishable macroscopic particles in canonical ensemble. This macroscopic particle, in which two or more atoms include, is literally a condensate that can be observed as an assembly in the system. In this case, we suppose all condensates are confined in the anisotropic parabolic trap and interaction between two condensates can be ignored by applying semi infinite cigar-shaped trap. It is also shown that the equation of state is indeed an ideal gas with the new thermodynamic interpretation of volume and pressure. Moreover, Even though our resulting partition function was portrayed as a sum of exponential functions, we prove that the series is indeed convergent.