# Thermalization in Solid-State NMR Controlled by Quantum Chaos in Spin Bath

## TL;DR

This paper demonstrates that in solid-state NMR, thermalization of carbon spins is driven by the collective chaotic dynamics of a distant proton spin bath, revealing the importance of many-body quantum chaos in spin diffusion.

## Contribution

It shows that proton spins far from carbon sites induce thermalization of $^{13}$C spins through collective chaos, a novel insight into spin diffusion mechanisms in solid-state NMR.

## Key findings

- Thermalization is driven by the collective dynamics of the proton spin bath.
- Chaos in the proton bath correlates with the onset of $^{13}$C spin thermalization.
- Far-away protons facilitate a network of strongly coupled spins that enable thermalization.

## 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 $^{13}$C nuclear spins, which interact via dipole-dipole coupling with the bath of strongly dipolar-coupled $^1$H 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 $^{13}$C spins, this interaction alone is not enough to drive spin diffusion and thermalize the $^{13}$C nuclear spins. We demonstrate that the thermalization within the $^{13}$C subsystem is driven by the collective many-body dynamics of the proton spin bath, and specifically, that the onset of thermalization among the $^{13}$C spins is directly related to the onset of chaotic behavior in the proton spin bath. Therefore, thermalization and spin diffusion within the $^{13}$C subsystem is controlled by the proton spins located far from the C sites. In spite of their weak coupling to the $^{13}$C spins, these far-away protons help produce a network of strongly coupled proton spins with collective dynamics, that drives thermalization.