  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.
