Delocalization of eigenfunctions in the banded random‑matrix Hamiltonian

Ascertain whether, for the Hamiltonian H_A + H_B + V with banded random-matrix interaction V = λR used in the study, the eigenfunctions are delocalized over the entire dynamically relevant Hilbert space, thereby clarifying the applicability of von Neumann’s H-theorem to the coarse-grained observational entropy in this setting.

Background

The authors discuss why von Neumann’s H-theorem does not appear to apply in their simulations, attributing the discrepancy to strong bandedness and insufficient confinement to a narrow energy shell. They posit that eigenfunctions may not be sufficiently delocalized over the relevant subspace.

However, they explicitly state that they cannot prove this due to computational limitations (lack of exact diagonalization), leaving the delocalization property of the eigenfunctions—and hence the rigorous applicability of the H-theorem—unresolved.