Critical Wetting Phase Transition in a Dilute Ternary Bose-Einstein Condensates

We investigate the possibility of a critical wetting phase transition in a dilute ternary Bose-Einstein condensate using Gross-Pitaevskii theory within the framework of the double parabola approximation. By analytically determining the condensate wave functions, we derive the dependence of the surfactant layer thickness on the intrinsic atomic parameters. Our results reveal conditions under which a critical wetting transition may occur, highlighting a new aspect of interfacial phenomena in multicomponent quantum fluids.