On the density-potential mapping in time-dependent density functional theory

TL;DR

This paper investigates the fundamental questions of uniqueness and existence in time-dependent density functional theory by addressing non-analytic potentials through a reformulation involving a non-linear Schrödinger equation with non-local potential dependence.

Contribution

It introduces a new formulation of TDDFT questions using a non-linear Schrödinger equation to handle non-analytic potentials, expanding the theoretical framework.

Findings

Addresses non-analytic potentials in TDDFT

Reformulates TDDFT questions via non-linear Schrödinger equation

Provides insights into potential non-locality in TDDFT

Abstract

The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to non-analyticities. We reformulate these questions in terms of a non-linear Schr\"odinger equation with a potential that depends non-locally on the wavefunction.