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arXiv · 1209.2949

Exact Density-Functionals with Initial-State Dependence and Memory

M. Ruggenthaler·S. E. B. Nielsen·R. van Leeuwen
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Abstract

We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two non-interacting 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 non-interacting 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 Schrödinger 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.

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M. Ruggenthaler, S. E. B. Nielsen, R. van Leeuwen. 2013-06-24. Exact Density-Functionals with Initial-State Dependence and Memory. https://doi.org/10.1103/physreva.88.022512

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