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 C2+ 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.Comment: 18 pages, 4 figure
