Quantal phase-space analysis of the driven surface-state electron

The quantum-mechanical phase space of the surface-state electron is studied in the presence of a time-dependent field, for which the classical dynamics has been shown to be chaotic. A coherent-state representation of the Wigner function for the surface-state electron Hamiltonian is constructed. This is then used to compare and contrast phase-space characteristics for quantum states initially in regular and irregular regions of the classical phase space. In particular, the effects of the driving frequency on the dynamics are examined in detail. We confirm that at larger frequencies, for a fixed field strength, the quantum phase-space evolution is restricted or localized. This localization is in contrast with the diffusive behavior still present in the classical evolution. The quantal evolution, at higher frequencies, appears better characterized by tunneling rather than by diffusion.