We study the non-equilibrium dynamics of a quantum generalization of a O(6) non-linear sigma model of competing orders in the underdoped cuprates (Hayward {\em et al.}, arXiv:1309.6639). We obtain results, in the large
N limit of a O(
N) model, on the time-dependence of correlation functions following a pulse disturbance. We find that the oscillatory responses share various qualitative features with recent optical experiments.
The line shape of photoemission spectra for underdoped cuprates is studied within the two-dimensional extended Hubbard model. Strong anisotropic scattering along the Fermi surface and the destruction of the Fermi surface near $(0,\ensuremath{\pi})$ are obtained for underdoped cuprates. These features are fully consistent with the recent angle-resolved photoemission experiments for underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ as well as with the recent QMC calculations.