The comprehensive study of the temperature dependent x-ray absorption spectroscopy (XAS) reveals a dynamical spectral weight $alpha$ in YBa$_2$Cu$_3$O$_y$ (YBCO). Large spectral weight changes for both the Upper Hubbard band and the Zhang-Rice band d
ue to dynamics of holes are experimentally found in the underdoped regime. A large value of $alpha geq 0.3$ is indispensable to describing XAS of YBCO with the conservation of states. The value of $alpha$ is linearly proportional to the pseudogap temperature in the underdoped regime, but becomes smaller as the doping level goes to the undoped limit. Our results clearly indicate that the pseudogap is related to the double occupancy and originates from bands in higher energies.
We propose and explore a stationary 1+log slicing condition for the construction of solutions to Einsteins constraint equations. For stationary spacetimes, these initial data will give a stationary foliation when evolved with moving puncture gauge co
nditions that are often used in black hole evolutions. The resulting slicing is time-independent and agrees with the slicing generated by being dragged along a time-like Killing vector of the spacetime. When these initial data are evolved with moving puncture gauge conditions, numerical errors arising from coordinate evolution are minimized. In the construction of initial data for binary black holes it is often assumed that there exists an approximate helical Killing vector that generates the binarys orbit. We show that, unfortunately, 1+log slices that are stationary with respect to such a helical Killing vector cannot be asymptotically flat, unless the spacetime possesses an additional axial Killing vector.
