  By means of quantum mechanics and quantum electrodynamics applied to coupled
harmonic Drude oscillators, we study the interaction between two neutral atoms
or molecules subject to a uniform static electric field. Our focus is to
understand the interplay between leading contributions to field-induced
electrostatics/polarization and dispersion interactions, as considered within
the employed Drude model for both non-retarded and retarded regimes. For the
first case, we present an exact solution for two coupled oscillators obtained
by diagonalizing the corresponding quantum-mechanical Hamiltonian and
demonstrate that the external field can control the strength of different
intermolecular interactions and relative orientations of the molecules. In the
retarded regime described by quantum electrodynamics, our analysis shows that
field-induced electrostatic and polarization energies remain unchanged (in
isotropic and homogeneous vacuum) compared to the nonretarded case. For
interacting species modeled by quantum Drude oscillators, the developed
framework based on quantum mechanics and quantum electrodynamics yields the
leading contributions to molecular interactions under the combined action of
external and vacuum fields.
