Planck's quantum-driven integer quantum Hall effect in chaos

TL;DR

This paper uncovers a Planck's quantum-driven topological quantum Hall effect in a chaotic system, revealing that chaos can give rise to quantized topological phenomena similar to those in quantum Hall systems.

Contribution

It demonstrates a novel topological quantum Hall effect emerging from chaos in a kicked spin-1/2 rotor, driven by Planck's quantum parameter, linking chaos and topological quantum phenomena.

Findings

Energy growth is unbounded at critical quantum values.

The phase is topologically characterized by quantized Hall conductance.

Number of conductance quanta jumps at critical points.

Abstract

The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Planck's quantum($h_e$)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of critical $h_e$-values, but otherwise bounded ('insulating' phase). The latter phase is topological in nature and characterized by a quantum number ('quantized Hall conductance'). The number jumps by unity whenever $h_e$ decreases passing through each critical value. Our findings, within the reach of cold-atom experiments, indicate that rich topological quantum phenomena may emerge from chaos.