  Dwarf nov\ae\ (DNe) and low mass X-ray binaries (LMXBs) are compact binaries
showing variability on time scales from years to less than seconds. Here, we
focus on explaining part of the rapid fluctuations in DNe, following the
framework of recent studies on the monthly eruptions of DNe that use a hybrid
disk composed of an outer standard disk and an inner magnetized disk. We show
that the ionization instability, that is responsible for the monthly eruptions
of DNe, is also able to operate in the inner magnetized disk. Given the low
density and the fast accretion time scale of the inner magnetized disk, the
ionization instability generates small, rapid heating and cooling fronts
propagating back and forth in the inner disk. This leads to quasi-periodic
oscillations (QPOs) with a period of the order of $1000$ s. A strong prediction
of our model is that these QPOs can only develop in quiescence or at the
beginning/end of an outburst. We propose that these rapid fluctuations might
explain a subclass of already observed QPOs in DNe as well as a, still to
observe, subclass of QPOs in LMXBs. We also extrapolate to the possibility that
the radiation pressure instability might be related to Type B QPOs in LMXBs.
