Exploratory X-ray Monitoring of Luminous Radio-Quiet Quasars at High
  Redshift: No Evidence for Evolution in X-ray Variability
  We report on the second installment of an X-ray monitoring project of seven
luminous radio-quiet quasars (RQQs). New {\sl Chandra} observations of four of
these, at $4.10\leq z\leq4.35$, yield a total of six X-ray epochs, per source,
with temporal baselines of $\sim850-1600$ days in the rest frame. These data
provide the best X-ray light curves for RQQs at $z>4$, to date, enabling
qualitative investigations of the X-ray variability behavior of such sources
for the first time. On average, these sources follow the trend of decreasing
variability amplitude with increasing luminosity, and there is no evidence for
X-ray variability increasing toward higher redshifts, in contrast with earlier
predictions of potential evolutionary scenarios. An ensemble variability
structure function reveals that their variability level remains relatively flat
across $\approx20 - 1000$ days in the rest frame and it is generally lower than
that of three similarly luminous RQQs at $1.33\leq z\leq 2.74$ over the same
temporal range. We discuss possible explanations for the increased variability
of the lower-redshift subsample and, in particular, whether higher accretion
rates play a leading role. Near-simultaneous optical monitoring of the sources
at $4.10\leq z\leq 4.35$ indicates that none is variable on $\approx1$-day
timescales, although flux variations of up to $\sim25$\% are observed on
$\approx100$-day timescales, typical of RQQs at similar redshifts. Significant
optical-X-ray spectral slope variations observed in two of these sources are
consistent with the levels observed in luminous RQQs and are dominated by X-ray
variations.
