Nuclear Spin Dynamics in Solids: Implications of Microscopic Chaos

Interaction between nuclear spins in solids forces each spin to perform a complicated dance in a time-dependent field created by neighboring spins. This leads to spin-spin relaxation observed by nuclear magnetic resonance (NMR). I briefly discuss the efforts to calculate NMR spin-spin relaxation from first principles, and then argue that the main obstacle to these efforts is the lack of the proper understanding of microscopic chaos. I proceed with presenting 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, and, in fact, were predicted on the basis of this analogy. Their discovery thus constitutes a new step in establishing the foundations of statistical physics. It suggests that, even in the situations, when quasi-classical chaotic limit is not tenable, and the spacing between energy levels is not relevant to the observable properties, the notion of microscopic chaos can be defined for isolated many-body quantum systems at the level of Pollicott-Ruelle resonances. [Refs.: B. V. Fine, Phys. Rev. Lett. v. 94, p. 247601 (2005); B. V. Fine, Int. J. Mod. Phys. B v. 18, p. 1119 (2004)]