[en] For the purpose of studying the mechanisms of hydrogen diffusion in separation devices e.g. transition-metal membranes, we have developed a microscopic dynamic model appropriate for describing the nonequilibrium statistical mechanics of hydrogen-in-a-metal. Using this model we have carried out a detailed analysis to obtain the autocorrelation function of density fluctuations in the model. Our model is built on the physical idea that, at low temperatures, spin clusters are the basic units or aggregates of transport. Our work can explain the reversed isotope effect in diffusion. We have also obtained an expression for the relative diffusivity, verifiable by experiments with tritium in metals. Our notion of spin clusters is novel. There is some evidence of their existence. The interstitial spin clusters are comparable to atomic and nuclear spin clusters, the only other natural spin clusters. Our demonstration of a long-time tail in the autocorrelation function is also novel. Diffusion can be anomalous if long time tails exist, a current topic in nonlinear behavior of fluids and solids. Our progress has been made possible by our development in the mathematical method of solving the generalized Langevin equation. This method is applicable to any time-dependent quantum many-body model. The underlying basis of this method is our discovery of a new orthogonalization process in Hilbert space, first since Gram and Schmidt over 100 years ago. Our process is simpler if Hilbert space is realized as is for all physical problems. To demonstrate the power and utility of our method we considered a well established model of metals, thereby discovering the existence of a low-frequency electronic mobility. This kind of intrinsic conductivity should exist in ensembles of all light particles, hence also relevant to hydrogen and its isotopes in metals