Local exchange-correlation vector potential with memory in time-dependent density functional theory: The generalized hydrodynamics approach

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Abstract
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.Comment: RevTex, 5 pages, no figures. Final version published in PR