Edge universality in Floquet sideband spectra

TL;DR

This paper demonstrates that the edge behavior of Floquet sideband spectra in non-interacting fermions exhibits universal patterns described by the Bessel and Airy kernels, with implications for shot-noise measurements.

Contribution

It establishes the universality of edge spectral statistics in Floquet systems and connects them to random matrix theory kernels, extending understanding of driven quantum transport.

Findings

Edge occupations follow the discrete Bessel kernel at any drive amplitude.

In large-amplitude regimes, the edge converges to the Airy kernel on an A^{1/3} scale.

Photo-assisted shot-noise slope deficit relates to the Airy kernel diagonal.

Abstract

We show that, for non-interacting fermions under a monochromatic phase drive (Tien--Gordon regime), the outgoing sideband occupations at a sharp Fermi edge are governed by the discrete Bessel kernel -- an exact result at any drive amplitude~$A$. In the large-amplitude regime the edge of this kernel converges, on the $A^{1/3}$ scale, to the Airy kernel of random matrix theory. This universality has a direct transport consequence: the deficit of the photo-assisted shot-noise slope from its high-bias plateau collapses onto the Airy-kernel diagonal. The derivation rests on a bridge between the linear detection chain and the Floquet scattering matrix: commensurate gating isolates a single coherence-order block of the one-body correlator. We identify the crossover temperature below which the Airy scaling is sharp, extend the analysis to biased two-terminal occupations, and argue that multi-tone drives make Pearcey-kernel cusps accessible in Floquet--Sambe space.