Inferring stealthy hyperuniform correlations from quantum transport

Abstract

Stealthy hyperuniform disordered systems exhibit strongly suppressed long-wavelength fluctuations, producing correlated disorder with unusual consequences for wave propagation. A central quantity characterizing these systems is the stealthiness parameter $χ$, which controls the range of excluded Fourier components in the disorder spectrum. However, in realistic settings, the microscopic disorder configuration may not be directly accessible, making it challenging to determine $χ$ from structural information alone. Here, we propose a conductance-based inverse protocol to recover stealthy hyperuniform correlations from transport data. As a proof of concept, we study spinless fermions in a one-dimensional tight-binding chain connected to clean semi-infinite leads, with on-site disorder generated by imposing a stealthy spectrum $S(k)=Θ(|k|-K)$, where $K=2πχ$. The energy-dependent transmittance is computed using a recursive Green's function method and compared with target spectra through a misfit function defined over an energy window. We show that the position of the sharp drop separating high- and low-transmittance regions is strongly controlled by $χ$, while the disorder strength $W$ mainly affects the absolute magnitude of the transmittance. As a result, the misfit function displays a clear minimum close to the target stealthy parameter. Our results demonstrate that transmittance spectra can serve as fingerprints of stealthy hyperuniform disorder, providing a practical route to infer correlated-disorder parameters from transport measurements.