  We study the Loschmidt echo for a system of electrons interacting through
mean-field Coulomb forces. The electron gas is modeled by a self-consistent set
of hydrodynamic equations. It is observed that the quantum fidelity drops
abruptly after a time that is proportional to the logarithm of the perturbation
amplitude. The fidelity drop is related to the breakdown of the symmetry
properties of the wave function.
