We study the motional narrowing of a spin-1/2 particle diffusing in a solid with random magnetic fields at sites. The crystal environment is modeled in a simple way interpolating between zero temperature and high temperatures. A two-site problem is solved exactly and the findings are in accordance with expectation. In the N-site problem the low temperature spin relaxation is found to be in striking contrast to the classical theory of motional narrowing. The relation to pSR experiments is discussed.
High temperature polysilicon (HTPS) projection engines provide a challenging environment for film-based optical components, especially the absorbing polarizers that are critical for image formation. Intrinsic polarizers do not contain unstable dichromophores and have been shown to be well suited for this application.
With the advent of advanced, automated fabrication techniques, the limiting factor in the production of complex aspheric space optics is increasing the ability to accurately measure and characterize optical surface parameters. In addition to increased accuracy, the metrology is required to keep pace with the shorter fabrication cycles of advanced figuring techniques such as computer-controlled polishing. As a result, there is an emphasis on:
1) Integrated testing approaches. Instruments such as interferometers must be interfaced with the polishing machine and the performance prediction software in order to minimize the time required to perform a full metrology cycle.
2) Redundancy in testing. Each surface parameter is measured in two independent, complementary test methods using unique test equipment. This minimizes the risk of systematic errors and reduces measurement uncertainty.
3) Overlapping measurement bandwidths. Test methods used to evaluate the surface errors are selected to ensure all spatial periods are adequately sampled and a complete characterization of the mirror surface is obtained.
We study the motional narrowing of a spin-(1/2) particle, diffusing in a solid with random magnetic fields at sites. At high temperatures, where the particle performs random walk between sites, the spin relaxes according to the well-known classical theory of motional narrowing. At low temperatures, where the particle is delocalized, we show that the classical theory breaks down. In this quantum regime we show that the tunnelling amplitude sets the scale for spin relaxation, but not the diffusion rate as previously thought.
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