Explicit solver for the electronic V-representation problem

TL;DR

This paper introduces an explicit solver for the time-dependent Kohn-Sham potential in TDDFT, providing new insights into lattice V-representability and enabling more detailed theoretical and numerical studies of quantum system evolution.

Contribution

It presents a novel explicit solver for the time-dependent Kohn-Sham potential and offers new characterizations of V-representability for one-electron systems.

Findings

New explicit solver for TDDFT potentials

Characterization of V-representability in one-electron systems

Numerical results demonstrating the solver's effectiveness

Abstract

One route to numerically propagating quantum systems is time dependent density functional theory (TDDFT). The application of TDDFT to a particular system's time evolution is predicated on V-representability which we have analyzed in a previous publication. In this work, we provide new insights concerning lattice V-representability using an newly developed explicit solver for the time-dependent Kohn-Sham potential which contrast with implicit solvers studied in the past few years. We present and interpret the force-balance equation central to our numerical method, describe details of its implementation, and present illustrative numerical results. A new characterization of V-representability for one-electron systems is also included. Taken together, the results here open the door to deeper theoretical and numerical investigations of the foundations of TDDFT.