  Recent developments in numerically exact quantum dynamics methods have
brought the dream of calculating the dynamics of chemically complex open
systems closer to reality. Path-integral-based methods, hierarchical equations
of motion (HEOM) and quantum analog simulators all require the spectral density
of the environment to describe its effect on the system. Here we find that the
rate of slow population relaxation is sensitive to the precise functional form
used to describe the spectral density peaks. This finding highlights yet
another challenge to obtaining accurate spectral densities. In the context of
quantum information science, we give a simple recipe to adjust the results of
analog simulation for this difference assuming both the simulator and the
target spectral densities are known.
