Hydrodynamic model of an inhomogeneous electron gas

We present a simple hydrodynamic model for the ground state of an inhomogeneous electron gas. The profile relation and response are obtained explicitly. In the case of a uniform reference system the profile relation reduces to that of the Sjölander-Stott theory. We confirm their results using the most recent numerical data. We compare numerical results for a heavy impurity problem in two dimensions with the corresponding results in three dimensions. A density modulation is conjectured to develop in the region just around a negative impurity at sufficiently low electron densities, as a signature of the Wigner transition.