Diffusion diffraction in disordered systems

We identify a new regime for the diffusion signal in non-confining disordered systems with locally varying diffusivity. It occurs at long times and large diffusion wavevectors, reminiscent of diffusion diffraction in closed pores. Remarkably, while for free diffusion the signal is exponentially strongly dephased, scattering off heterogeneities results in a much weaker, power-law decrease of the signal, thereby offering an enhanced sensitivity to the medium’s structure. In particular, we show how correlation functions of the medium’s microstructure to arbitrary order can be measured. We compare our theoretical predictions for the second order correlation function to numerical simulations with good agreement.