  We study the competition between one-body and two-body couplings in
weakly-interacting two-component Bose gases, in particular as regards field
correlations. We derive the meanfield theory for both ground state and
low-energy pair excitations in the general case where both one-body and
two-body couplings are position-dependent and the fluid is subjected to a
state-dependent trapping potential. General formulas for phase and density
correlations are also derived. Focusing on the case of homogeneous systems, we
discuss the pair-excitation spectrum and the corresponding excitation modes,
and use them to calculate correlation functions, including both quantum and
thermal fluctuation terms. We show that the relative phase of the two
components is imposed by that of the one-body coupling, while its fluctuations
are determined by the modulus of the one-body coupling and by the two-body
coupling. One-body coupling and repulsive two-body coupling cooperate to
suppress relative-phase fluctuations, while attractive two-body coupling tends
to enhance them. Further applications of the formalism presented here and
extensions of our work are also discussed.
