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

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.

18 pages, 4 figures

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• Quantum Electrodynamical Density-Functional Theory: Bridging Quantum Optics and Electronic-Structure Theory
• A brief compendium of time-dependent density-functional theory
• Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system
• Time-dependent density-functional theory for real-time electronic dynamics on material surfaces
• Probing quantum coherence in ultrafast molecular processes: an ab initio approach to open quantum systems
• How Electronic Dynamics with Pauli Exclusion Produces Fermi-Dirac Statistics
• Measuring excitation-energy transfer with a real-time time-dependent density functional theory approach
• A correlated-polaron electronic propagator: open electronic dynamics beyond the Born-Oppenheimer approximation