Many-body quantum dynamics by the reduced density matrix based on the time-dependent density functional theory

TL;DR

This paper develops a method to evaluate the many-body quantum density matrix using time-dependent density functional theory, revealing significant differences from traditional approaches in photoemission processes.

Contribution

It introduces a novel approach to compute the reduced density matrix within TDDFT, incorporating off-diagonal elements for more accurate many-body quantum dynamics analysis.

Findings

Quantitative differences in photoemission predictions compared to Fermi's golden rule.

First-order exchange theory applied to quasi-2D electron gas and atoms.

Highlights importance of off-diagonal density matrix elements in quantum processes.

Abstract

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 G\"{o}rling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant $\lambda$ naturally arises. We then find the reduced density matrix $\rho_\lambda({\bf r},{\bf r}',t)$, which, by construction, has the $\lambda$-independent diagonal elements $\rho_\lambda({\bf r},{\bf r},t)=n({\bf r},t)$, $n({\bf r},t)$ being the particle density. The off-diagonal elements of $\rho_\lambda({\bf r},{\bf r}',t)$ contribute importantly to the processes, which cannot be treated 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 $\lambda$, 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.