  Electron dynamics in metallic clusters are examined using a time-dependent
density functional theory that in-cludes a "memory term", i.e. attempts to
describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn
exchange-correlation (XC) kernel we construct a translationally invariant
memory action from which an XC potential is derived that is translationally
covariant and exerts zero net force on the electrons. An efficient and stable
numerical method to solve the resulting Kohn-Sham equations is presented. Using
this framework, we study memory effects on electron dynamics in spherical
Jellium "gold clusters". We find memory significantly broadens the surface
plasmon absorption line, yet considerably less than measured in real gold
clusters, attributed to the inadequacy of the Jellium model. Two-dimensional
pump-probe spectroscopy is used to study the temporal decay profile of the
plasmon, finding a fast decay followed by slower tail. Finally, we examine
memory effects on high harmonic generation, finding memory narrows emission
lines.
