Open quantum dynamics theory for Coulomb potentials: Hierarchical equations of motion for atomic orbitals (AO-HEOM)

We investigate the quantum dynamics of Coulomb potential systems in thermal baths. We study these systems within the framework of open quantum dynamics theory, focusing on preserving the rotational symmetry of the entire system, including the baths. Thus, we employ a three-dimensional rotationally invariant system-bath model to derive numerically "exact" hierarchical equations of motion for atomic orbitals that enable a non-perturbative and non-Markovian treatment of system-bath interactions at finite temperatures. To assess the formalism, we calculated the linear absorption spectrum of an atomic system under an isotropic thermal environment, with systematic variation of system-bath coupling strength and temperature.