Complex scattering dynamics and the integral quantum hall effect

The effect of a magnetic field on potential scattering is investigated microscopically. A magnetic field renders the scattering of a classical charged particle far more complex than previously suspected. Consequences include possible 1/f{hook} noise and an explanation of the observed breakdown of the quantum Hall effect at large currents. A particular scattering center is described by a discontinuous one-dimensional Hamiltonian map, a class of maps that has not previously been studied. A renormalization group analysis indicates that singular behavior arises from the interplay of electron orbits that are periodic and orbits that are quasiperiodic.