  First, we define phase tropical hypersurfaces in terms of a degeneration data
of smooth complex algebraic hypersurfaces in $(\mathbb{C}^*)^n$. Next, we prove
that complex hyperplanes are diffeomorphic to their degeneration called phase
tropical hyperplanes. More generally, using Mikhalkin's decomposition into
pairs-of-pants of smooth algebraic hypersurfaces, we show that phase tropical
hypersurfaces with smooth tropicalization, possess naturally a smooth
differentiable structure. Moreover, we prove that phase tropical hypersurfaces
possess a natural symplectic structure.
