Dependence of operator Krylov complexity on the smearing profile

Analyze systematically how retaining nonzero spatial Fourier modes and varying the spatial smearing profile affect the spectral measure, Lanczos coefficients, and late-time operator Krylov complexity of the spatially smeared boundary operators in the two-sided BTZ geometry.

Background

The operator Krylov analysis is carried out explicitly in the zero spatial Fourier mode, where the dependence on the smearing width drops out. The paper notes that nonzero Fourier modes can reintroduce dependence on the detailed smearing profile, potentially affecting the spectral measure and the Lanczos sequence. A systematic treatment is left unresolved.