geraintpalmer
commented
2 years ago What about in more than one dimension? Then there is more than one boundary state (e.g. (1, B), (2, B), ... (B-1, B), (B, B)). Let $\tilde{B}$ denote the set of boundary states.
Do we:
- Take $H{R\tilde{B}} = \max{i \in R, b \in \tilde{B}} \left( h{ib} \right)$ ? That is $H{RB}$ is the highest probability of hitting a boundary state from the reasonable region.
- Or Take $H{R\tilde{B}} = \max{i \in R} \left( \cup{b \in \tilde{B}} h{i b} \right)$ ? That is $H_{RB}$ is the probability of hitting any of the boundary states from the reasonable region.
Note that $\max+{i \in R} \left( h_{iB} \right)$ does not actually take a
max, as the states are ordered, it's the hitting probability from the 'highest' state in the reasonable region.