Optimal complexity for multi-band

Background: The complexity analysis for approximating BCFs by sums of exponentials is largely dependent on the type of spectral singularity present in the bath environment.

Question / Future Work: The paper analytically determines the complexity scaling with simulation time $T$ based on the singularity order $\alpha$ of the spectral density. Future work involves applying this framework to multi-band systems, but the optimal complexity scaling in terms of the number of bands remains an open question.