  We study one dimensional quasiperiodic system obtained from the tight-binding
model on the square lattice in a uniform magnetic field with the spin orbit
interaction. The phase diagram with respect to the Harper coupling and the
Rashba coupling are proposed from a number of numerical studies including a
multifractal analysis. There are four phases, I, II, III, and IV in this order
from weak to strong Harper coupling. In the weak coupling phase I all the wave
functions are extended, in the intermediate coupling phases II and III mobility
edges exist, and accordingly both localized and extended wave functions exist,
and in the strong Harper coupling phase IV all the wave functions are
localized. Phase I and Phase IV are related by the duality, and phases II and
III are related by the duality, as well. A localized wave function is related
to an extended wave function by the duality, and vice versa. The boundary
between phases II and III is the self-dual line on which all the wave functions
are critical. In the present model the duality does not lead to pure spectra in
contrast to the case of Harper equation.
