Electronic properties of the 1D Frenkel-Kontorova model

The energy spectra and quantum diffusion of an electron in a 1D incommensurate Frenkel-Kontorova (FK) model are studied numerically. We found that the spectral and dynamical properties of electron display quite different behaviors in invariance circle regime and in Cantorus regime. In the former case, it is similar to that of the Harper model, whereas in the latter case, it is similar to that of the Fibonacci model. The relationship between spectral and transport properties is discussed.