  Quasi-two-dimensional (2D) systems, such as an electron gas confined in a
quantum well, are important model systems for many-body theories. Earlier
studies of the crossover from 3D to 2D in ground-state density-functional
theory showed that local and semilocal exchange-correlation functionals which
are based on the 3D electron gas are appropriate for wide quantum wells, but
eventually break down as the 2D limit is approached. We now consider the
dynamical case and study the performance of various linear-response exchange
kernels in time-dependent density-functional theory. We compare approximate
local, semilocal and orbital-dependent exchange kernels, and analyze their
performance for inter- and intrasubband plasmons as the quantum wells approach
the 2D limit. 3D (semi)local exchange functionals are found to fail for quantum
well widths comparable to the 2D Wigner-Seitz radius, which implies in practice
that 3D local exchange remains valid in the quasi-2D dynamical regime for
typical quantum well parameters, except for very low densities.
