Domains of time-dependent density-potential mappings

TL;DR

This paper establishes new mathematical conditions for the existence and uniqueness of the density-potential mapping in time-dependent density functional theory, broadening the class of densities that can be represented.

Contribution

It provides rigorous conditions and constructs a weighted Sobolev space to ensure solutions, expanding the set of v-representable densities in the theory.

Findings

Conditions for existence and uniqueness are established.

The class of v-representable densities is significantly expanded.

A new mathematical framework using weighted Sobolev spaces is introduced.

Abstract

The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches this mapping is transformed into a certain type of Sturm-Liouville problem. Here we give conditions for existence and uniqueness of solutions and construct the weighted Sobolev space they lie in. As a result the class of v-representable densities is considerably widened with respect to previous work.