Time-dependent exchange-correlation current density functionals with memory

TL;DR

This paper develops a time-dependent density functional theory approach that incorporates memory effects into exchange-correlation functionals, aiming to improve the accuracy of electron dynamics simulations beyond the adiabatic approximation.

Contribution

It introduces a memory-dependent functional consistent with known properties of the electron gas, derived from a Galilean invariant action principle for time-dependent electron density and velocity.

Findings

Functional includes memory effects beyond adiabatic approximation

Ensures causality and Galilean invariance in the equations

Aligns with known properties of the homogeneous electron gas

Abstract

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e. the effective potential at time t is determined solely by the density at the same time. This paper discusses a method that aims to go beyond this approximation, by incorporating "memory" effects: the potential will depend also on the history. We add to the adiabatic approximation an additional part that includes memory and yields a functional that is totally consis-tent with known dynamical properties of the homogeneous electron gas (in the linear response limit). In order to achieve this, we write down an action principle from which Kohn-Sham equations are derived for description of the time-dependent electron density and fluid velocity field. The action principle is built in such a way that it is Galilean invariant and yields causal equations.