  We report the discovery of coupling between periodic and aperiodic
variability and ~12-mHz X-ray quasi-periodic oscillations (QPOs) from the X-ray
binary pulsar Her X-1 using data from the Rossi X-Ray Timing Explorer. We found
two different couplings, one during the pre-eclipse dips and the other during
the normal state of the source, using a method which directly compares the
low-frequency power-density spectra (PDS) with those of the sidebands around
the coherent pulse frequency. The pre-eclipse dip lightcurves show significant
time variation of photon counts, and this variation appears in the PDS as both
strong mHz powers and well-developed sidebands around the coherent pulse
frequency. The linear correlation coefficients between the mHz PDS and the
sideband PDS obtained from two pre-eclipse dip data segments are 0.880 +- 0.003
and 0.982 +- 0.001, respectively. This very strong coupling demonstrates that
the amplitudes of the coherent pulsations are almost exactly modulated by the
aperiodic variabilities, suggesting that both the periodic and aperiodic
variabilities are related to time variation of obscuration of X-rays from the
central pulsar by an accretion disk during pre-eclipse dips. We also found weak
coupling during the normal state of the source, together with ~12-mHz QPOs. The
normal state coupling seems to reconcile with the prediction that the aperiodic
variabilities from X-ray binary pulsars are due to time-varying accretion flows
onto the pulsar's magnetic poles. If the ~12-mHz QPOs are due to global-normal
disk oscillations caused by the gravitational interactions between the central
pulsar and the accretion disk, the inferred inner-disk radius is roughly
comparable to the magnetospheric radius, ~1 10^8 cm.
