  We propose a semi-classical approach based on the Vlasov equation to describe
the time-dependent electronic dynamics in a bulk simple metal under an
ultrashort intense laser pulse. We include in the effective potential not only
the ionic Coulomb potential and mean-field electronic Coulomb potential from
the one-body electron distribution but also the exchange-correlation potential
within the local density approximation (LDA). The initial ground state is
obtained by the Thomas-Fermi model. To numerically solve the Vlasov equation,
we extend the pseudo-particle method, previously used for nuclei and atomic
clusters, to solids, taking the periodic boundary condition into account. We
apply the present implementation to a bulk aluminum (FCC) conventional unit
cell irradiated with a short laser pulse. The optical conductivity, refractive
index, extinction coefficient, and reflectivity as well as energy absorption
calculated with the Vlasov-LDA method are in excellent agreement with the
results by the time-dependent density functional theory and experimental
references.
