Local exchange-correlation vector potential with memory in Time-Dependent Density Functional Theory: the generalized hydrodynamics approach

TL;DR

This paper develops a nonlinear, non-adiabatic approximation for the exchange-correlation vector potential in time-dependent density functional theory, based on Landau Fermi liquid theory and hydrodynamics, accounting for memory effects.

Contribution

It introduces a novel local functional form for the xc vector potential using a stress tensor approach derived from generalized hydrodynamics.

Findings

Derivation of a nonlinear non-adiabatic xc vector potential

Reduction to a metric-dependent form for irrotational motion

Framework applicable to systems with evolving momentum fields

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.