 Material-density damping of a Gross–Pitaevskii condensate

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.