  We present a detailed account of the technical aspects of stochastic quantum
molecular dynamics, an approach introduced recently by the authors [H. Appel
and M. Di Ventra, Phys. Rev. B 80 212303 (2009)] to describe coupled
electron-ion dynamics in open quantum systems. As example applications of the
method we consider both finite systems with and without ionic motion, as well
as describe its applicability to extended systems in the limit of classical
ions. The latter formulation allows the study of important phenomena such as
decoherence and energy relaxation in bulk systems and surfaces in the presence
of time-dependent fields.
