Dispersion of incoherent spectral features in systems with strong electron-phonon coupling

We study (inverse) photoemission from systems with strong coupling of doped carriers to phonons. Using an adiabatic approximation, we develop a method for calculating spectra. This method is particularly simple for systems where the electron-phonon coupling can be neglected in the initial state, e.g., the undoped t-J model. The theory then naturally explains why the electron-phonon coupling just leads to a broadening of spectra calculated without electron-phonon coupling, without changing the dispersion. This is in agreement with recent angle-resolved photoemission spectroscopy (ARPES) on undoped cuprates, and it supports the interpretation in terms of strong electron-phonon interaction. The theory also shows that for systems with strong electron-phonon coupling in the initial state, the result cannot in general be related to the spectrum obtained without electron-phonon coupling.