Local exchange-correlation vector potential with memory in   Time-Dependent Density Functional Theory: the generalized hydrodynamics   approach
  Using Landau Fermi liquid theory we derive a nonlinear non-adiabatic approximation for the exchange-correlation (xc) vector potential defined by the xc stress tensor. The stress tensor is a local nonlinear functional of two basic variables - the displacement vector and the second-rank tensor which describes the evolution of momentum in a local frame moving with Eulerian velocity. For irrotational motion and equilibrium initial state the dependence on the tensor variable reduces to that on a metrics generated by a dynamical deformation of the system. 
I. V. Tokatly and O. Pankratov