WavePacket vs. WaveTrain (24-Jan-2023)

After our WaveTrain software (on GitHub since 28-May-2022) has been formally integrated into our WavePacket software package as the third sub-project last December, the time was ripe for a thorough comparison of the two packages. For the example of phonons in a chain-like quasi-1D setup and also for excitons coupled to phonons we have set up and described a few test calculations, along with critical discussions. The good news in short form: for short chains (up to 6 sites), the results from the two approaches are (approximately) equal, as expected. While the visualization may be more appealing with WavePacket, the transition to longer chains is only possible with WaveTrain, due to the very favorable scaling of storage requirement and numerical effort of the underlying tensor-train based techniques, thus mitigating the curse of dimensionality.