Quantum transmission in 1D disordered stealthy hyperuniform Kronig--Penney-like models

Disordered stealthy hyperuniform (SHU) systems are emerging as platforms for controlling classical and quantum transport due to vanishing single-scattering contributions in the stealthy regime. Here, to our knowledge, we present the first perturbation theory of one-dimensional quantum transport through a continuum of identical point scatterers with SHU positional disorder. Our perturbation theory indicates the exact cancellation of all the lower-order terms due to the Fourier-space stealthy condition $S(q)=0$, and the further suppression of the lowest non-vanishing fourth order in the Lyapunov exponent $\lambda (k)$ due to the real-space hyperuniform constraint $\underset{D\to \mathrm{\infty }}{\lim }{\sigma }_D^2=c<\mathrm{\infty }$. Our findings presents universal implications of the general wave-propagation phenomena in disordered SHU systems.