  We investigate the coupling of an inhomogeneous electron system to phonons.
The properties of an electronic system composed of a mixture of microscopic
ordered and disordered islands are changed fundamentally by a phonon mode. In
high-Tc cuprates, such a phase separation scenario is supported by recent STM
and nuclear quadrupole resonance studies. We show that even a weak or moderate
electron-phonon coupling can be sufficient to produce dramatic changes in the
electronic state of the inhomogeneous electron gas. The spectral properties
calculated in our approach provide a natural explanation of the low-energy
nodal ARPES features and exhibit a novel non-Fermi-liquid state stabilized
through electron-phonon coupling.
