Ref. Cornering the universal shape of fluctuations, https://pubmed.ncbi.nlm.nih.gov/35022397/ Nature Communications, 2022, vol. 13, issue 1, 1-7

“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 the 3D boundary into independent 1D conduction channels. This foliation is extremely sensitive to the confining potential and generically yields chaotic flows. Here we study the quantum correlations and entanglement of such edge modes in 4D droplets confined by harmonic traps, whose boundary is a squashed three-sphere.”

Ergodic Edge Modes in the 4D Quantum Hall Effect, https://hal.archives-ouvertes.fr/hal-03203619

First email: 30 December 2022

Dear Prof. Dr. Benoit Estienne:

May we ask, “What is the geometry of squashed three-spheres?” Perhaps, a better question is “From where did these squashed three-spheres originate?”  Is it that they are squashed or that it is part of the geometries of gaps?  Thank you.

Most sincerely,

Bruce