Many-Body Quantum Dynamics by the Reduced Density Matrix Based on Time-Dependent Density-Functional Theory

We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of Görling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant λ naturally arises. We then find the reduced density matrix ρλ(r,r′,t), which, by construction, has the λ independent diagonal elements ρλ(r,r,t)=n(r,t), n(r,t) being the particle density. The off-diagonal elements of ρλ(r,r′,t) contribute importantly to the processes unaccessible via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in λ, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.