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Chaotic eigenmodes of nuclear spin dynamics in solids

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Boris Fine, Physics Department, University of Tennessee
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I present a theory, which invokes the notion of chaos and thereby predicts that NMR free induction decay and spin echoes observed in the same system have identical exponential long-time behavior. This prediction was shown to be quantitatively correct by a very recent NMR experiment on hyperpolarized solid xenon. Such a lack of dependence of the long-time decay on the initial spin configuration reveals a new fundamental property of nuclear spin dynamics in solids. Namely, the quantum time evolution operator of a macroscopic system of nuclear spins 1/2 has isolated eigenmodes, which govern the long-time relaxation towards equilibrium. These eigenmodes decay on the ballistic microscopic timescale. Therefore, their existence cannot be predicted using the standard approximations of statistical physics. Such eigenmodes, however, are very reminiscent of Pollicott-Ruelle resonances in classical chaotic systems.