Dependence on the unfolding prescription

Characterize how the choice of spectral unfolding prescription affects unfolded Krylov complexity, particularly for finite systems and spectra near singularities.

Background

Spectral unfolding removes the smooth density of states, but in practical applications the smooth density or cumulative density must generally be estimated numerically. Different smoothing prescriptions can therefore produce different unfolded spectra.

The authors identify the dependence of unfolded Krylov complexity on this prescription as unresolved, especially when the spectrum is finite or contains spectral singularities.

References

Several questions remain open. Our analysis focused primarily on the infinite-temperature TFD state, for which the spectral weights are uniform. It would be interesting to determine how the picture changes at finite temperature or for more general initial states, where nontrivial spectral weights provide an additional source of structure. The dependence on the unfolding prescription, particularly in finite systems or near spectral singularities, also deserves further study.

— Unfolded Krylov complexity: universal chaotic dynamics without false positives  (2609.02228 - Erdmenger et al., 2 Sep 2026) in Section 7, Discussion

Several questions remain open. Our analysis focused primarily on the infinite-temperature TFD state, for which the spectral weights are uniform. It would be interesting to determine how the picture changes at finite temperature or for more general initial states, where nontrivial spectral weights provide an additional source of structure. The dependence on the unfolding prescription, particularly in finite systems or near spectral singularities, also deserves further study. More broadly, extending these ideas to operator Krylov complexity would require identifying the appropriate unfolding of the Liouvillian spectral measure and could clarify whether saddle-dominated exponential growth can be filtered in an analogous way.

— Unfolded Krylov complexity: universal chaotic dynamics without false positives  (2609.02228 - Erdmenger et al., 2 Sep 2026) in Section 7, Discussion