Electronic structure of solids with competing periodic potentials

When electrons are subject to a potential with two incommensurate periods, translational invariance is lost, and no periodic band structure is expecte d. However, model calculations based on nearly free one-dimensional electro ns and experimental results from high-resolution photoemission spectroscopy on a quasi-one-dimensional material do show dispersing band states with si gnatures of both periodicities. Apparent band structures are generated by t he nonuniform distribution of electronic spectral weight over the complex e igenvalue spectrum.