Multiple phonon branches

[jarvist]

You have a load of half interpreted versions of this in various lab books. So you should actually implement it.
The basic idea is to put multiple phonon branches in the 'true' Lagrangian, against which the model v and w Lagrangian is varied. This should give more temperature dependent structure in the e.g. mobility curves, as individual phonon modes go into resonance.

• figure out a nice way to go from i.r. activity + frequency to dielectric constant contribution
• units? interface with a VASP script? Intermediate .dat file to keep interface cleanly separate?
• implement this simply as a set of contributions to the Frohlich Hamiltonian, used in the calculation of a single v and w polaron at finite T.
• if this is too expensive, consider some variational approximation where you first project the complex spectra onto a representative set of modes
• stare at the results
• compare and contrast to the Hellwarth1999 averaging techniques
• sort out the Hellwarth1999 A scheme (finite temperature). Half implemented in a Jupyter notebook somewhere?
• see whether you can treat mode lifetime (i.e. from Phonopy3) at the same time, by adding a Gaussian width to the resonance