Hydrodynamic approach to coherent nuclear spin transport

TL;DR

This paper develops a hydrodynamic linear response formalism to analyze nuclear spin diffusion in dipolar solids, comparing theoretical predictions with experimental results and discussing discrepancies in energy diffusion.

Contribution

It introduces a systematic expansion of Kubo's formula for calculating diffusion coefficients, offering advantages over previous methods and applying it to nuclear spin transport.

Findings

The formalism agrees with experiments for magnetization diffusion.

Discrepancies are observed between theory and experiment for energy diffusion.

Possible reasons for the disparity are discussed.

Abstract

We develop a linear response formalism for nuclear spin diffusion in a dipolar coupled solid. The theory applies to the high-temperature, long-wavelength regime studied in the recent experiments of Boutis et al. [Phys. Rev. Lett. 92, 137201 (2004)], which provided direct measurement of interspin energy diffusion in such a system. A systematic expansion of Kubo's formula in the flip-flop term of the Hamiltonian is used to calculate the diffusion coefficients. We show that this approach is equivalent to the method of Lowe and Gade [Phys. Rev. 156, 817 (1967)] and Kaplan [Phys. Rev. B 2, 4578 (1970)], but has several calculational and conceptual advantages. Although the lowest orders in this expansion agree with the experimental results for magnetization diffusion, this is not the case for energy diffusion. Possible reasons for this disparity are suggested.