Phase-Space Explorations in Time-Dependent Density Functional Theory

TL;DR

This paper explores extending time-dependent density functional theory to phase-space densities to better address challenges in ionization momentum distributions and memory effects, demonstrated through two-electron model systems analyzed with Wigner functions.

Contribution

It proposes a phase-space density functional theory extension to TDDFT, aiming to improve accuracy in ionization and memory-dependent dynamics.

Findings

Exact numerical solutions of two-electron models in phase-space

Analysis using Wigner function distributions

Potential improvements in TDDFT approximations

Abstract

We discuss two problems which are particularly challenging for approximations in time-dependent density functional theory (TDDFT) to capture: momentum-distributions in ionization processes, and memory-dependence in real-time dynamics. We propose an extension of TDDFT to phase-space densities, discuss some formal aspects of such a "phase-space density functional theory" and explain why it could ameliorate the problems in both cases. For each problem, a two-electron model system is exactly numerically solved and analysed in phase-space via the Wigner function distribution.