The Riemann hypothesis is a major open problem in number theory. It asserts that the nontrivial zeros of the Riemann zeta function $\zeta \left(x\right)$ occur on the critical line, i.e., for $x=u+iy$ with $u=\frac{1}{2}$, in the complex plane. We discuss the physical realization of the zeros of $\zeta \left(x\right)$ on the critical line by means of a 1D nonperiodic lattice with sites at positions $z_j=dln(j+1)$ $(j\in \{0,1,2,...\left\}\right)$ along the $z$ axis with $d$ a length and the form factors of the sites modulated by ${(-1)}^{j+1}{e}^{-\alpha z_j}$ with $\alpha d$ playing the role of $u$. On the critical line, $\alpha d=\frac{1}{2}$. We find quasitransparent states when $y=\frac{kd}{2}$ is the imaginary part of a zero of $\zeta \left(x\right)$ on the critical line with $k$ the wave vector of the particle between sites $z_j$ and $z_{j+1}$.

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• 1-dimensional systems
• Quasicrystals
• Landauer formula