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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 Plancks quantum($h_e$)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotors 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.
A highly non-thermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance
Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here we shed f
We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for various groun
We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $sigma_{xy} = pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively c
Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with fl