Correlation and coherence order screening

[fidgetspinner]

Hey!

When specifying the basis set, Spinach gives an option for conserving the coherence order by setting the parameter bas.projections. I would like to preserve only the terms corresponding to zero-quantum coherence, so therefore I have specified:

bas.projections = 0;

The behavior to me is unexpected. Here is a demonstration using a dipolar-copuled two-spin system. When bas.projections is not defined, I get the full relaxation matrix, shown in the picture.

full.jpg (29.44 KiB) Viewed 73834 times

By setting bas.projections = 0, the I was expecting to see the first block. However, it seems that the term T_10T_10 (coherence order 0) is missing from the basis set, resulting in relaxation matrix shown in the other picture.

zqc.jpg (7.86 KiB) Viewed 73834 times

Am I misunderstanding the purpose of bas.projections? What would be the correct procedure of preserving only the first block corresponding to coherence order 0?

Any help is greatly appreciated!

[kuprov]

This is a subtle consequence of first truncating the basis and only then calculating the relaxation superoperator.

Think about it: Redfield superoperator is a double commutator - a state might go somewhere out of the ZQ subspace in the first commutator, and then come back into the ZQ subspace in the second one. Thus, the presence of other states would have an indirect effect on the ZQ block of the relaxation superoperator. However, if the basis is truncated before the double commutator is taken, the above cannot happen, and so some terms would be lost.

Therefore, the correct procedure is to calculate the relaxation superoperator in the complete basis and then project the result into the ZQ subspace.