Master equation and cluster perturbation theory based approaches to correlated open quantum systems in nonequilibrium

Masahito Ueda

Alan A. Dzhioev, Daniel S. Kosov

We develop a superoperator coupled cluster method for nonequilibrium open many-body quantum systems described by the Lindblad master equation. The method is universal and applicable to systems of interacting fermions, bosons or their mixtures. We present a general theory and consider its application to the problem of quantum transport through the system with electron–phonon correlations. The results are assessed against the perturbation theory and nonequilibrium configuration interaction theory calculations.

Martin Eckstein, Andreas Hackl, Stefan K. Kehrein +4 more

David G. Tempel, Mark A. Watson, Roberto Olivares-Amaya +1 more

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary 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 noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the 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 including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. 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 the Görling-Levy perturbation theory is calculated.

David G. Tempel, Mark A. Watson, Roberto Olivares‐Amaya +1 more

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary 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 noninteracting open Kohn–Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the 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 including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. 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 the Görling–Levy perturbation theory is calculated.

Enrico Arrigoni