Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system

TL;DR

This paper investigates the properties of exact functionals in open quantum systems time-dependent density functional theory (OQS-TDDFT) using an exactly-solvable one-electron model to understand relaxation and dephasing effects.

Contribution

It provides insights into the properties of exact OQS-TDDFT functionals through analysis of a solvable model, highlighting challenges in developing approximate functionals.

Findings

Exact properties of OQS-TDDFT functionals deduced from the model

Analysis of relaxation and dephasing limits in open quantum systems

Discussion of challenges in functional approximation for many-electron systems

Abstract

The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum systems time-dependent density functional theory (OQS-TDDFT) within the master equation approach were established. It was proven that the exact time-dependent density of a many-electron open quantum system evolving under a master equation can be reproduced with a closed (unitarily evolving) and non-interacting Kohn-Sham system. This potentially offers a great advantage over previous approaches to OQS-TDDFT, since with suitable functionals one could obtain the dissipative open-systems dynamics by simply propagating a set of Kohn-Sham orbitals as in usual TDDFT. However, the properties and exact conditions of such open-systems functionals are largely unknown. In the present article, we examine a simple and exactly-solvable model open quantum system: one electron in a harmonic well evolving under the Lindblad master equation. We examine two different representitive limits of the Lindblad equation (relaxation and pure dephasing) and are able to deduce a number of properties of the exact OQS-TDDFT functional. Challenges associated with developing approximate functionals for many-electron open quantum systems are also discussed.