= Material-density damping of a Gross–Pitaevskii condensate
{title2=$-i\psi_t=\tfrac12\nabla^2\psi+(1-|\psi|^2)\psi-\zeta\psi D_n|\psi|^2$}
Let $D_n=\partial_t+\mathbf v_n\cdot\nabla$ be the <material derivative> of the <normal fluid>, and $\zeta>0$. The displayed phenomenological density damping preserves the condensate <continuity equation> because its coefficient is real. Under a <Galilean boost>, both velocities shift by the boost velocity and the field acquires the Schrödinger phase; $D_n|\psi|^2$ is invariant. Thus the normal-fluid derivative, rather than a derivative along the condensate flow, is essential to the model.
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