Many-body quantum dynamics by the TDDFT-based theory of the density matrix

Vladimir U. Nazarov

Published 2018-09-11Version 1

We introduce a method of evaluating 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 [G\"{o}rling and Levy, Phys. Rev. A {\bf 50}, 196 (1994), G\"{o}rling, ibid. {\bf 55}, 2630 (1997)], from which the expansion of the density matrix in powers of the interaction constant $\lambda$ naturally arises. By this, we obtain the one-density-matrix $\rho_\lambda(\rv,\rv',t)$, which, by construction, has the $\lambda$-independent diagonal elements $\rho_\lambda(\rv,\rv,t)=n(\rv,t)$, where $n(\rv,t)$ is the particle density. The off-diagonal elements of $\rho_\lambda(\rv,\rv',t)$ importantly contribute to the processes beyond the reach of TDDFT, of which we consider the momentum-resolved photoemission, doing this to the first order in $\lambda$ (exact exchange). In an illustrative calculation of photoemission from the quasi-2D electron gas with {\it one filled subband} we find strong deviations from the independent-particle Fermi golden rule formula.