Thesis defense of Timo Gräßer

The high-temperature dynamics of spin systems is crucial in a number of modern research areas such as nitrogen-vacancy centers in diamond and nuclear magnetic resonance. This doctoral thesis deals with a dynamic mean-field theory, dubbed spinDMFT, that allows for the simulation of such systems. The relatively modest computational expense of the method permits an extension to spin clusters (CspinDMFT), which increases both the accuracy and the computational effort. CspinDMFT is employed to simulate the dynamics of randomly-distributed defect spins on a diamond surface. The interplay between effective dipolar anisotropy and positional disorder results in a significant difference between the timescales of longitudinal and transverse relaxation. This phenomenon has also been observed experimentally. In another part of this work, spinDMFT and an extension to non-local correlations (nl-spinDMFT) are used to simulate nuclear magnetic resonance experiments such as the free induction decay and spin echoes. The agreement with experimental data for calcium fluoride (CaF2) and adamantane (C10H16) is excellent. An interesting outlook in this context is the extension to magic-angle-spinning experiments which are highly relevant in solid-state nuclear magnetic resonance spectroscopy with high precision. The central conclusion of this thesis is that spinDMFT and its extensions are limited to high temperatures, but offer computationally cheap and highly flexible numerical methods which are applicable to a wide range of systems in this limit.