Quantum transmission in 1D disordered stealthy hyperuniform Kronig–Penney-like models
Published in arXiv, 2026
Disordered stealthy hyperuniform (SHU) systems are emerging as platforms for controlling classical and quantum transport because single-scattering contributions vanish 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 lower-order terms due to the Fourier-space stealthy condition $S(q)=0$, and further suppression of the lowest nonvanishing contribution, at fourth order, to the Lyapunov exponent $\lambda(k)$ due to the real-space hyperuniform constraint $\lim_{D\to\infty}\sigma_D^2=c<\infty$. Our findings have universal implications for wave propagation in disordered SHU systems.
Recommended citation: Yuan, S., Vanoni, C., Torquato, S. (2026). "Quantum transmission in 1D disordered stealthy hyperuniform Kronig--Penney-like models." arXiv:2610.02501 .
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