  In recent years, ultrafast pump-probe spectroscopy has provided insightful
information about nonequilibrium dynamics of excitations in materials. In a
typical experiment of time-resolved x-ray absorption spectroscopy, the systems
are excited by a femtosecond laser pulse (pump pulse) followed by an x-ray
(probe pulse) after a time delay to measure the absorption spectra of the
photoexcited systems. We present a theory for nonequilibrium x-ray absorption
spectroscopy in one-dimensional strongly correlated systems. The core hole
created by x-ray is modeled as an additional effective potential of the core
hole site which changes the spectrum qualitatively. In equilibrium, the
spectrum reveals the charge gap at half-filling and the metal-insulator
transition in the presence of the core hole effect. Furthermore, a pump-probe
scheme is introduced to drive the system out of equilibrium before the x-ray
probe. The effects of the pump pulse with varying frequencies, shapes and
fluences are discussed for the dynamics of strongly correlated systems in and
out of resonance. The spectrum indicates that the driven insulating state has a
metallic droplet around the core hole. The rich structures of the
nonequilibrium x-ray absorption spectrum give more insight into the dynamics of
electronic structures.
