  Time-resolved X-ray Emission/Absorption Spectroscopy (Tr-XES/XAS) is an
informative experimental tool sensitive to electronic dynamics in materials,
widely exploited in diverse research fields. Typically, Tr-XES/XAS requires
X-ray pulses with both a narrow bandwidth and sub-picosecond pulse duration, a
combination that in principle finds its optimum with Fourier transform-limited
pulses. In this work, we explore an alternative xperimental approach, capable
of simultaneously retrieving information about unoccupied (XAS) and occupied
(XES) states from the stochastic fluctuations of broadband extreme ultraviolet
pulses of a free-electron laser. We used this method, in combination with
singular value decomposition and Tikhonov regularization procedures, to
determine the XAS/XES response from a crystalline silicon sample at the
L2,3-edge, with an energy resolution of a few tens of meV. Finally, we combined
this spectroscopic method with a pump-probe approach to measure structural and
electronic dynamics of a silicon membrane. Tr-XAS/XES data obtained after
photoexcitation with an optical laser pulse at 390 nm allowed us to observe
perturbations of the band structure, which are compatible with the formation of
the predicted precursor state of a non-thermal solid-liquid phase transition
associated with a bond softening phenomenon.
