Quantum-Spin Diffusion Driven by Ergodic and Non-Ergodic Finite Spin Baths

We investigate spin diffusion driven by a finite quantum spin bath in a system accessible for solid-state NMR experiments; namely polycrystalline L-alanine. The direct spin transport within the subsystem consisting of dipolar coupled carbon spins is suppressed due to disorder given by different Larmor frequencies. Spin diffusion is, therefore, governed by the surrounding network of proton spins-1/2. This proton network consists of strongly coupled groups which are weakly interacting among each other. By means of numerical simulations, we model realistic solid-state NMR experiments. We show that nearby proton spins govern the local magnetic field for carbon spins, while the farther proton spins determine dynamics within the proton bath. In particular, the farther proton spins provide ergodicity in the proton bath and, thereby, drastically change the spin diffusion in the carbon subsystem. We also consider deuterated alanine with all proton spins-1/2 replaced by deuteron spins-1. For deuterated L-alanine, we show that the local magnetic fields created by deuterons is insufficient to allow for spin diffusion due to the small magnetic dipole moment of deuterons. Instead, spin diffusion is governed by the spin-lattice relaxation of deuteron spins on much larger time scales.