1209.2949 (M. Ruggenthaler et al.)

Exact Density-Functionals for Correlated Dynamics on a Quantum Ring    [PDF]

M. Ruggenthaler, S. E. B. Nielsen, R. van Leeuwen

We explicitly construct the time-dependent Kohn-Sham potential as a functional of the density and the initial state for the case of a quantum ring with two interacting particles in a singlet state. We show that for this case the initial state is completely determined by the initial density, the initial time-derivative of the density and a single integer that characterizes the (angular) momentum of the system. We give an exact expression for the exchange-correlation potential that produces the exact density of a noninteracting reference system with a different initial state. This is used to demonstrate that the Kohn-Sham procedure correctly predicts the density of a reference system without the need of solving the reference system's Schr\"odinger equation. We further construct the exchange-correlation potential and frequency-dependent exchange-correlation kernel for an analytically solvable system of two electrons on a quantum ring with a squared cosine two-body interaction. This constitutes an exact benchmark-system for future approximations in time-dependent density-functional theory.

View original: http://arxiv.org/abs/1209.2949