Extracting bath information from open-quantum-system dynamics with the hierarchical equations-of-motion method

We present a simple and effective approach for extracting the bath information in open-quantum-system dynamics under the framework of the numerically exact hierarchical equations-of-motion method, for which it is usually not straightforward to adjust the boundary between the system and bath. The key component of our approach is an additional bath mode that weakly interacts with the system through the same coupling channel as the mode of interest, which we call the probe mode. By combining the probe mode with the system and calculating its expectation value, we can deduce the corresponding expectation value of the mode of interest via simple relations. The effectiveness of our approach is demonstrated by exact decomposition of dissipation by a continuous spectral density.