Magnetic-field-controlled electron dynamics in quantum cavities

Although soft confinement of electrons in ballistic cavities gives rise to a power law of classical probability distributions, the behavior is limited to a narrow range of the variable if the potential is not substantially smooth. The presence of a magnetic field normal to the cavity extends the power-law regime by generating a hierarchical phase space structure. The change in dynamics induced by the magnetic field is confirmed experimentally through analysis of conductance fluctuations in quantum cavities defined by electrostatic gates on a high-mobility heterojunction. Nonfractal conductance fluctuations as a function of the gate bias at zero magnetic field are transformed to be fractal when the cyclotron radius is comparable to the cavity size.