3 research outputs found
Analytic density-functionals with initial-state dependence and memory
We analytically construct the wave function that, for a given initial state, produces a prescribed density for
a quantum ring with two noninteracting particles in a singlet state. In 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 then give an exact analytic expression for the exchange-correlation
potential that relates two noninteracting systems with different initial states. This is used to demonstrate how the
Kohn-Sham procedure predicts the density of a reference system without the need of solving the reference system’s
Schrodinger equation. We further numerically construct the exchange-correlation potential for an analytically ¨
solvable system of two electrons on a quantum ring with a squared cosine two-body interaction. For the same
case we derive an explicit analytic expression for the exchange-correlation kernel and analyze its frequency
dependence (memory) in detail. We compare the result to simple adiabatic approximations and investigate the
single-pole approximation. These approximations fail to describe the doubly excited states, but perform well in
describing the singly excited states.peerReviewe