Many-body dynamics in nuclear spin diffusion

Since its introduction by Bloembergen in 1949, nuclear spin diffusion has been a topic of significant interest in magnetic resonance. Spin diffusion, which can be defined as the transfer of spin polarisation induced by the dipolar interaction, is a ubiquitous transport mechanism in solids. Experimental observations of spin diffusion contain structural information. However, the many-body nature of the problem makes it difficult to describe from first principles. The central goal of this thesis is to obtain a quantitative description of the spin diffusion phenomenon from first-principles, through the development of suitable models of the underlying many-body dynamics. To that end we first consider an extension of an existing approach that relies on a master equation to describe the polarisations, for the case of proton-driven carbon-13 spin diffusion (PDSD). Second, a novel approach is introduced for the simulation of the time evolution of selected observables for large strongly coupled nuclear spin systems, using low-order correlations in Liouville space (LCL). Following the introduction of this new simulation method, Liouville-space reduction in solids is analysed in more detail, in order to identify the conditions under which the LCL approximation is valid. Finally, using the LCL model, simulations of proton spin diffusion (PSD) and PDSD are performed, directly from crystal geometry and with no adjustable parameters, and are found to be in excellent agreement with experimental measurements for polycrystalline organic solids.