  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.
