I stumbled upon an issue trying to simulate 7Li spins in two-site chemical exchange where each nucleus is in the slow tumbling regime.
When trying to identify the reasonable equilibrium density (as the population-weighted average of individual 7Li equilibrium polarization) and force the system to reach that state after a perturbation (via thermalize.m), the system doesn't go back exactly to the targeted state.
Instead, higher rank tensors (with otherwise initial low populations) are building up until they reach a non-negligible steady state. From multiple attempted scenarios, it looks like they build up as a consequence of cross-relaxation pathways enabled by either quadrupolar (T10<->T30) or CSA/Q cross-correlation (T10<->T20) at the two chemical sites. Though one can think of this as the result of 1st site's polarization behaving as a non-equilibrium (hyper)polarization in the 2nd site's environment (with different mixing pathways) and vice-versa until a new state is achieved, the result itself seems unrealistic. It would imply that, at thermal equilibrium, there are already non-zero T20 and T30 types of populations due solely to relaxation and exchange dynamics.
Other approaches without thermalizing the relaxation superoperator resulted in the density operator decaying towards 0, despite assuming Dibari-Levitt thermalization.
I upload here one notebook highlighting this phenomenon. Also, it looks like the unity operator in the targeted (realistic) density operator is already set correctly to 1.
I would appreciate any help on how solve this issue.
Thank you once more for this incredibly useful software you and your collaborators developed,
Florin Teleanu