Abstract
Most applications of time-dependent density-functional theory (TDDFT)
use the adiabatic local-density approximation (ALDA) for the dynamical
exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic)
extension of the ground-state LDA into the dynamical regime leads
to a Vxc(r,t) 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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