Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential . An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schrödinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems but becomes correct in the thermodynamic limit.
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Research Article| December 21 2006
Time-dependent density-functional theory beyond the adiabatic approximation: Insights from a two-electron model system
C. A. Ullrich; Time-dependent density-functional theory beyond the adiabatic approximation: Insights from a two-electron model system. J. Chem. Phys. 21 December 2006; 125 (23): 234108. https://doi.org/10.1063/1.2406069
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