Dynamic approach to local-polarization distribution and NMR line shape in deuteron glasses.

The path-integral formulation of Glauber dynamics by Sommers is applied to calculate the deuteron NMR line shape in structural glasses such as ${\mathrm{Rb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{ND}}_{4}$${)}_{\mathit{x}}$${\mathrm{D}}_{2}$${\mathrm{PO}}_{4}$. The system is described by a classical pseudospin Ising model with infinite-range exchange interactions and quenched random electric fields. It is shown that in the fast-motion limit the NMR line shape is directly related to the average probability distribution of local deuteron polarization and that the observable truncated second moment of the NMR line ${\mathit{M}}_{2}^{\mathrm{tr}}$ is proportional to the Edwards-Anderson order parameter ${\mathit{q}}_{\mathrm{EA}}$. Leading dynamic corrections due to the slowing down of deuteron jumps in the ergodic phase are evaluated, and the behavior of ${\mathit{M}}_{2}^{\mathrm{tr}}$ at the crossover between the fast- and the slow-motion regimes is discussed.