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Random walk to and interaction with an impurity

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Abstract

A random walker tagged with a spin may conveniently be studied by small amounts of paramagnetic impurities which significantly affect the spin relaxation at concentrations as low as a few parts per million. Examples are found in nuclear magnetic resonance (NMR) and muon spin rotation (μSR). At low temperature relaxation is determined by the time for the walker to reach an impurity, and thus the impurity acts like a simple trap. Details of the interaction with the impurity are important at higher temperatures, and the relaxation rate is shown to go through a maximum because of this. Special features associated with many returns to the origin, particularly important in one-dimensional walks, and the difference between incoherent (rapidly fluctuating paramagnetic spin) and coherent (stationary paramagnetic spin) returns are discussed.

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Authors and Affiliations

  1. Sandia National Laboratories, 87185, Albuquerque, New Mexico

    Peter M. Richards

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  1. Peter M. Richards
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Additional information

This work performed at Sandia National Laboratories supported by the U.S. Department of Energy under contract No. DE-AC04-76DP000789.

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Richards, P.M. Random walk to and interaction with an impurity. J Stat Phys 30, 497–507 (1983). https://doi.org/10.1007/BF01012323

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  • DOI: https://doi.org/10.1007/BF01012323

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