Superfluid velocity
= Superfluid velocity
{title2=$\mathbf u=(\hbar/m)\nabla S$}
For a condensate $\psi=\sqrt n e^{iS}$ with kinetic operator $-\hbar^2\nabla^2/(2m)$, 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 $D=1/2$.