  The dissipative quantum mechanics of a charged particle in a uniform magnetic
field and periodic potential has delocalization critical points which
correspond to backgrounds for the open string. We study the phase diagram of
this system (in the magnetic field/dissipation constant plane) and find a
fractal structure which, in the limit of zero dissipation, matches the fractal
energy level structure of the pure quantum mechanical version of this problem
(Hofstadter model).
