Superfluid velocity ($\mathbf{u}=(\hslash /m)\nabla S$)

For a condensate $\psi =\sqrt{n}{e}^{iS}$ with kinetic operator $-{\hslash }^2{\nabla }^2/(2m)$, its particle current is $n\mathbf{u}$ with the displayed velocity. This follows by subtracting the Gross–Pitaevskii equation from its complex conjugate. More generally, in units where the kinetic operator is $-D{\nabla }^2$, the current velocity is $2D\nabla S$. The complex argument gradient and current velocity coincide only when $D=1/2$.