Time-Dependent Density Functional Theory of Open Quantum Systems in the Linear-Response Regime

TL;DR

This paper extends linear-response time-dependent density functional theory (TDDFT) to open quantum systems described by a master equation, enabling the calculation of broadened and shifted electronic excitation spectra in non-unitary environments.

Contribution

It develops a formulation of LR-TDDFT for open quantum systems, deriving a pseudo-eigenvalue equation with complex energies and Lamb shifts, and demonstrates it on a C$^{2+}$ atom in a photon bath.

Findings

Successfully calculated broadened spectra of an open quantum system.

Analyzed the performance of an adiabatic exchange-correlation kernel.

Derived a first-order frequency-dependent correction to Kohn-Sham linewidth.

Abstract

Time-Dependent Density Functional Theory (TDDFT) has recently been extended to describe many-body open quantum systems (OQS) evolving under non-unitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a non-interacting open Kohn-Sham system yielding the correct non-equilibrium density evolution. A pseudo-eigenvalue equation analogous to the Casida equations of usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C$^{2+}$ atom in an optical resonator interacting with a bath of photons. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on Gorling-Levy perturbation theory is calculated.