  We study the time lags between the continuum emission of quasars at different
wavelengths, based on more than four years of multi-band ($g$, $r$, $i$, $z$)
light-curves in the Pan-STARRS Medium Deep Fields. As photons from different
bands emerge from different radial ranges in the accretion disk, the lags
constrain the sizes of the accretion disks. We select 240 quasars with
redshifts $z \approx 1$ or $z \approx 0.3$ that are relatively emission line
free. The light curves are sampled from day to month timescales, which makes it
possible to detect lags on the scale of the light crossing time of the
accretion disks. With the code JAVELIN, we detect typical lags of several days
in the rest frame between the $g$ band and the $riz$ bands. The detected lags
are $\sim 2-3$ times larger than the light crossing time estimated from the
standard thin disk model, consistent with the recently measured lag in NGC5548
and micro-lensing measurements of quasars. The lags in our sample are found to
increase with increasing luminosity. Furthermore, the increase in lags going
from $g-r$ to $g-i$ and then to $g-z$ is slower than predicted in the thin disk
model, particularly for high luminosity quasars. The radial temperature profile
in the disk must be different from what is assumed. We also find evidence that
the lags decrease with increasing line ratios between ultraviolet FeII lines
and MgII, which may point to changes in the accretion disk structure at higher
metallicity.
