  An approach to correlated dynamics of quantum nuclei and electrons both in
dynamical interaction with external environments is presented. This stochastic
quantum molecular dynamics rests on a theorem that establishes a one-to-one
correspondence between the total ensemble-averaged current density of
interacting nuclei and electrons and a given external vector potential. The
theory allows for a first-principles description of phenomena previously
inaccessible via standard quantum molecular dynamics such as electronic and
nuclear relaxation in photochemistry, dissipative correlated electron-ion
dynamics in intense laser fields, nuclear dephasing, etc. As a demonstration of
the approach, we discuss the rotational relaxation of
4-(N,N-dimethylamino)benzonitrile in a uniform bath in the limit of classical
nuclei.
