  A method to derive the charge current density and its quantum mechanical
correlation from the scattering matrix is discussed for quantum scattering
systems described by a time-dependent Hamiltonian operator. The current density
and charge density are expressed with the help of functional derivatives with
respect to the vector potential and the electric potential. A condition imposed
by the requirement that these local quantities are gauge invariant is
considered. Our formulas lead to a direct relation between the local density of
states and the total current density at a given energy. To illustrate the
results we consider, as an example, a chiral ladder model.
