Many-body quantum dynamics by the TDDFT-based theory of the reduced density matrix
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 [Gorling and Levy, Phys. Rev. A {\bf 50}, 196 (1994), Gorling, ibid. {\bf 55}, 2630 (1997)], from which the expansion of the density matrix in powers of the interaction constant $\lambda$ naturally arises. We then find the reduced density matrix $\rho_\lambda(\rv,\rv',t)$, which, by construction, has the $\lambda$-independent diagonal elements $\rho_\lambda(\rv,\rv,t)=n(\rv,t)$, $n(\rv,t)$ being the particle density. The off-diagonal elements of $\rho_\lambda(\rv,\rv',t)$ contribute importantly to the processes beyond the reach of TDDFT, of which we consider the momentum-resolved photoemission, doing this to the first order in $\lambda$, i.e., on the level of exact exchange. In an illustrative calculation of photoemission from the quasi-2D electron gas we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi golden rule formula.