Exact Density-Functionals with Initial-State Dependence and Memory

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.

12 pages, 5 figures

References in corpus (5)

• Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory
• Is time-dependent density functional theory formally exact?
• Global fixed point proof of time-dependent density-functional theory
• Density-potential mappings in quantum dynamics
• Periodicity of the time-dependent Kohn-Sham equation and the Floquet theorem

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• Kinetic and potential components of the exact time-dependent correlation potential
• Time-Dependent Density Functional Theory Beyond Kohn-Sham Slater Determinants
• A Snapshot of Time-Dependent Density-Functional Theory
• Exact time-dependent density functional theory for non-perturbative dynamics of helium atom
• Time-dependent density-functional theory for strongly interacting electrons
• Insights From Exact Exchange-Correlation Kernels
• Ultra-nonlocality in density functional theory for photo-emission spectroscopy
• Invertibility of retarded response functions for Laplace transformable potentials: application to one-body reduced density matrix functional theory
• Strictly correlated electrons approach to excitation energies of dissociating molecules