  A stochastic approach to time-dependent density functional theory (TDDFT) is
developed for computing the absorption cross section and the random phase
approximation (RPA) correlation energy. The core idea of the approach involves
time-propagation of a small set of stochastic orbitals which are first
projected on the occupied space and then propagated in time according to the
time-dependent Kohn-Sham equations. The evolving electron density is exactly
represented when the number of random orbitals is infinite, but even a small
number (? 16) of such orbitals is enough to obtain meaningful results for
absorption spectrum and the RPA correlation energy per electron. We implement
the approach for silicon nanocrystals (NCs) using real-space grids and find
that the overall scaling of the algorithm is sublinear with computational time
and memory.
