  We develop a dielectric matrix and analyze plasmon dispersion in strongly
coupled charged-particle bilayers in the quantum domain. The formulation is
based on the classical quasi-localized charge approximation (QLCA) and extends
the QLCA formalism into the quantum domain. Its development, which parallels
that of 2D companion paper [Phys. Rev. E 70, 026406 (2004)] by three of the
authors, generalizes the single-layer scalar formalism therein to a bilayer
matrix formalism. Using pair correlation function data generated from diffusion
Monte Carlo simulations, we calculate the dispersion of the in-phase and
out-of-phase plasmon modes over a wide range of in-layer coupling values and
layer spacings. The out-of-phase spectrum exhibits an exchange-correlation
induced long-wavelength energy gap in contrast to earlier predictions of
acoustic dispersion softened by exchange-correlations. The energy gap is
similar to what has been previously predicted for classical charged-particle
bilayers and subsequently confirmed by recent molecular dynamics computer
simulations.
