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The spectral response and physical features of the 2D Hubbard-Holstein modelare calculated both in equilibrium at zero and low chemical dopings, and afteran ultra short powerful light pulse, in undoped systems. At equilibrium and atstrong charge-lattice couplings, the optical conductivity reveals a 3-peakstructure in agreement with experimental observations. After an ultra shortpulse and at nonzero electron-phonon interaction, phonon and spin subsystemsoscillate with the phonon period $T_{ph} \approx 80$ fs. The decay time of thephonon oscillations is about 150-200 fs, similar to the relaxation time of thecharge system. We propose a criterion for observing these oscillations in high$T_c$ compounds: the time span of the pump light pulse $\tau_{pump}$ has to beshorter than the phonon oscillation period $T_{ph}$.

Quantum Dynamics of the Hubbard-Holstein Model in Equilibrium and Non-Equilibrium: Application to Pump-Probe Phenomena