Complex Classical and Quantum Scattering Dynamics and the Quantum Hall Effect

The effect of a magnetic field on potential scattering is investigated microscopically. Analytic, exact renormalization-group, and numerical solutions show that the classical scattering dynamics of a charged particle is extremely complex. In one case, the dynamics is described by a discontinuous one-dimensional Hamiltonian map. Preliminary results indicate complex quantum dynamics as well. Consequences include an explanation of the observed breakdown of the quantum Hall effect at large currents and possible $\frac{1}{f}$ noise.