Ergodic edge modes in the 4D quantum Hall effect

The gapless modes on the edge of four-dimensional (4D) quantum Hall droplets are known to be anisotropic: they only propagate in one direction, foliating 3D boundary into independent 1D conduction channels. This foliation is extremely sensitive confining potential and generically yields chaotic flows. Here we study correlations entanglement such 4D confined by harmonic traps, whose a squashed three-sphere. Commensurable trapping frequencies lead periodic trajectories electronic guiding centers; corresponding independently along $S^1$ fibers, forming bundle conformal field theories over 2D base space. By contrast, incommensurable produce quasi-periodic, ergodic trajectories, each which covers its invariant torus densely; correlation function has fractal features. wealth behaviors highlights sharp differences between their peers; it also exhibits dependence choice trap, suggesting existence observable bifurcations due droplet deformations.