Eigensolutions of the kicked Harper model

Abstract

The time-evolution operator for the kicked Harper model is reduced to block matrix form when the effective Planck's constant hbar = 2 pi M/N and M and N are integers. Each block matrix is spanned by an orthonormal set of N "kq" (quasi-position/quasi-momentum) functions. This implies that the system's eigenfunctions or stationary states are necessarily discrete and periodic. The reduction allows, for the first time, an examination of the 2-dimensional structure of the system's quasi-energy spectrum and the study of, with unprecedented accuracy, the system's stationary states.