Phys. Rev. Lett. (in the press); preprint at http://arxiv.org/abs/1706.00019
In relativistic systems, information propagation is bounded by the speed of light, giving rise to the light-cone structure in Minkowski spacetime. A similar constraint exists in non-relativistic local quantum spin systems, known as the Lieb–Robinson bound. This provides a maximum propagation speed of entanglement and correlation, in turn leading to an effective spacetime light-cone. Now Thomas Hartman and colleagues have shown that consistency of diffusive transport with this light-cone places an upper bound on diffusivity.
Relating three independent quantities — diffusivity, equilibration timescale and light-cone velocity — this upper bound is found to hold in a variety of physical systems in both regimes of strong and weak coupling. The result has wide implications, including a generalization of the Drude formula giving the lower bound of electrical resistivity in the absence of long-lived quasiparticles, and a relation between hydrodynamic and leading non-hydrodynamic modes in black holes. It will also motivate more systematic studies — for example, using ultracold quantum gases and unconventional metals, for simultaneous determination of the three quantities involved in setting the bound.
Rights and permissions
About this article
Cite this article
Li, Y. Bounded diffusion. Nature Phys 13, 926 (2017). https://doi.org/10.1038/nphys4294