Universal stability of coherently diffusive one-dimensional systems with respect to decoherence

Static disorder in a three-dimensional 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 paradigmatic one-dimensional models, namely, the Harper-Hofstadter-Aubry-André and Fibonacci tight-binding chains, along with 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 coherently 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 to the mean elastic scattering time. Thus, systems with a quantum diffusive regime could be used to design robust quantum wires. Moreover, our results might shed light on the functionality of many biological systems, which often operate at the border between the ballistic and localized regimes.