  A first principle theory of charge transport in spatially inhomogeneous
quantum systems composed of any finite number of particles and subject to weak
electro-magnetic fields is developed. Simple analytical expressions for the
linear contributions to the quantum susceptibilities and conductivity tensors,
and the charge and current densities of such systems are derived in terms of
two-time Green's functions. The obtained results can be applied to description
of quantum charge transport in any finite system, including small semiconductor
quantum dots, artificial molecules and atoms, etc.
  PACS: 05.60.Cg, 05.30.-d, 03.65Yz, 73.63.-b, 03.65.Db
