Universal stability of coherently diffusive 1D systems with respect to decoherence
Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localized regime. This Metal-Insulator Transition is often preceded by coherent diffusion. By studying three different paradigmatic 1D models, the Harper-Hofstadter-Aubry-Andr\'e and the Fibonacci tight-binding chains, and the power-banded random matrix model, we show that whenever coherent diffusion is present, transport is exceptionally stable against decoherent noise. This is completely at odds with what happens for ballistic and localized dynamics, where the diffusion coefficient strongly depends on the environmental decoherence. A universal dependence of the diffusion coefficient on the decoherence strength is analytically derived: the diffusion coefficient remains almost decoherence-independent until the coherence time becomes comparable with the mean elastic scattering time. Thus, systems with a quantum diffusive regime could be used to design stable quantum wires and may explain the functionality of many biological systems, which often operate at the border between the ballistic and localized regimes.