Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function

In open-system approaches with non-Markovian environments, the process of inserting an individual mode (denoted as pseudomode) into the bath or extracting it from the bath is widely employed. This procedure, however, is typically performed on basis of the spectral density and does not incorporate temperature. Here, we show how the (temperature-dependent) bath correlation function (BCF) transforms in such a process. We present analytic formulas for the transformed BCF and numerically study the differences between factorizing initial state and global thermal (correlated) initial state of mode and bath, respectively. We find that in the regime of strong coupling of the mode to both system and bath, the differences in the BCFs give rise to pronounced differences in the dynamics of the system.