Quantum wells in tilted fields: Semiclassical analysis and experimental evidence for effects “beyond” periodic orbits

Quantum wells in tilted fields are of great current interest as experimental probes of the transition to chaos in a mesoscopic system. Here we carry out an analysis of quantal and experimental periodic orbit (PO) amplitudes for tilt angles $\theta =11\mathrm{}°$ and $27°$. We calculate stability parameters and test the quantal and experimental results against a recently proposed theoretical periodic orbit formula. We find that many experimental features are understood in terms of torus states, ghosts, and bifurcations rather than isolated periodic orbits. We analyze previously unexplained jumps in period-one current at low fields and show these to be due to the changes in the quantum number of the most accessible torus state. We estimate that about one-quarter of the $I-V$ oscillations in these experiments are dominated by ghost contributions (complex periodic orbits). We find that only a small fraction of bifurcations of accessible periodic orbits are visible experimentally. Agreement with the simplified PO formula is only qualitative and the limitations of the theory are discussed.