Prevalence of the adiabatic exchange-correlation potential approximation in time-dependent density functional theory

TL;DR

This paper demonstrates that the adiabatic exchange-correlation potential approximation in time-dependent density functional theory remains valid even under high-frequency, ultra-strong electric fields, contrary to common assumptions.

Contribution

It reveals that the adiabatic approximation is rigorously applicable to finite electron systems exposed to extreme fields, challenging the belief that memory effects always dominate.

Findings

Adiabatic XCPF is valid in high-frequency, ultra-strong fields for finite systems.

Supports previous numerical results on 1D helium atom under strong laser pulses.

Applicable to any number of electrons and in full 3D environments.

Abstract

Time-dependent (TD) density functional theory (TDDFT) promises a numerically tractable account of many-body electron dynamics provided good simple approximations are developed for the exchange-correlation (XC) potential functional (XCPF). The theory is usually applied within the adiabatic XCPF approximation, appropriate for slowly varying TD driving fields. As the frequency and strength of these fields grows, it is widely held that memory effects kick in and the eligibility of the adiabatic XCPF approximation deteriorates irreversibly. We point out however that when a finite system of electrons in its ground-state is gradually exposed to a very a high-frequency and eventually ultra-strong homogeneous electric field, the adiabatic XCPF approximation is in fact rigorously applicable. This result not only helps to explain recent numerical results for a 1D-helium atom subject to a strong linearly-polarized laser pulse (Thiel et al, Phys. Rev. Lett. 100, 153004, (2008)) but also shows that it is applicable to any number of electrons and in full 3D.