Abstract
We theoretically investigate thermalization and spin diffusion driven by a quantum spin bath for a realistic solid-state NMR experiment. We consider polycrystalline L-alanine, and investigate how the spin polarization spreads among several ¹³C nuclear spins, which interact via dipole-dipole coupling with the bath of strongly dipolar-coupled ¹H nuclear (proton) spins. We do this by using direct numerical simulation of the many-spin time-dependent Schr\"odinger equation. We find that, although the proton spins located near the carbon sites interact most strongly with the ¹³C spins, this interaction alone is not enough to drive spin diffusion and thermalize the ¹³C nuclear spins. We demonstrate that the thermalization within the ¹³C subsystem is driven by the collective many-body dynamics of the proton spin bath, and specifically, that the onset of thermalization among the ¹³C spins is directly related to the onset of chaotic behavior in the proton spin bath. Therefore, thermalization and spin diffusion within the ¹³C subsystem is controlled by the proton spins located far from the C sites. In spite of their weak coupling to the ¹³C spins, these far-away protons help produce a network of strongly coupled proton spins with collective dynamics, that drives thermalization.