  We investigate the spectral and timing properties of the millihertz
quasi-periodic oscillations (mHz QPOs) in neutron-star low-mass X-ray binary 4U
1636-53 using XMM-Newton and Rossi X-ray Timing Explorer (RXTE) observations.
The mHz QPOs in the XMM-Newton/RXTE observations show significant frequency
variation and disappear right before type I X-ray bursts. We find no
significant correlation between the mHz QPO frequency and the temperature of
the neutron-star surface, which is different from theoretical predictions. For
the first time we observed the full lifetime of a mHz QPO lasting 19 ks.
Besides, we also measure a frequency drift timescale around 15 ks, we speculate
that this is the cooling timescale of a layer deeper than the burning depth,
possibly heated by the previous burst. Moreover, the analysis of all X-ray
bursts in this source shows that all type I X-ray bursts associated with the
mHz QPOs are short, bright and energetic, suggesting a potential connection
between mHz QPOs and He-rich X-ray bursts.
