百科页面 'Partial Overlaps of Many Body Wavefunctions' 删除后无法恢复,是否继续?
Eigenstates are mutually orthogonal when integrated over the whole space. One can however ask “how” orthogonal states are, by looking at the overlap computed over a fraction of space (for example, particles confined to one side of the system).
Expectation: all pairs of states are mutually orthogonal, but some are more orthogonal than others.
Formally, one can start from
$$ PO_{ab} (s) = \int_0^{L-s} dx \psi^\dagger_a \psi_b $$
with $s$ between $0$ and $L$.
For which systems can this partial overlap be computed exactly? For integrable systems?
Is this a smarter way to distinguish localized systems from delocalized ones?
Is this a way to define a physically relevant “distance” between wavefunctions? (for example, $dPO/ds$ around $s = 0$, or any other measure really).
This is complementary to entanglement entropy, but in a sense much more physical.
百科页面 'Partial Overlaps of Many Body Wavefunctions' 删除后无法恢复,是否继续?