SPECTRAL PROPERTIES OF A SIMPLE HAMILTONIAN MODEL

The spectral properties of a Hamiltonian dependent on a parameter alph a are investigated. Due to the linearity in momentum and periodicity i t was possible to strengthen some known results for the analogous kick ed model. It is rigorously shown that, for any potential in a ''large' ' set, the spectrum is pure for each fixed value of alpha. Depending o n the arithmetic character of alpha the spectrum is pure absolutely co ntinuous, pure singular continuous, or pure point. It is also shown th at in some sense the classical dynamics is identical to the quantum on e.