Implement the "lone phonon" method

[matthewcarbone]

One nice generalization of the MA family is allowing a phonon to be created at a larger distance away from the main cloud. This is another one of Mona/Stepan's requests and will be a very nice option for users who wish to implement a more specific type of GGCE.

Particularly, I envision that the model will be passed some extra option kwargs. For example, the new Model.add_ signature might look something like

def add_(
    self,
    coupling_type,
    phonon_frequency,
    phonon_extent,
    phonon_number,
    phonon_extent_tfd=None,
    phonon_number_tfd=None,
    coupling_strength=None,
    dimensionless_coupling_strength=None,
    phonon_index_override=None,
    secondary_phonon_extent=None,   # new!
    secondary_phonon_number=None    # new!
)

Where the parameter secondary_phonon_number will control the number of phonons that are allowed to be "farther away" (where 1 is what was initially suggested, but there's no reason we can't generalize that!), and secondary_phonon_extent will control just how far away from the main cloud these extra phonons can go.

[Chiffafox]

This looks good to me, that's the way to go! Agreed about the two key controlling parameters of number and extent of secondary phonon.

I would just add that MA has already been generalized to an arbitrary number of "lone phonons": it is part of the variational hierarchy, along with cloud size. This is the foundational reference, and this is the reference where it is formulated in the "modern" way, a.k.a. in real space -- this is actually the 2010 reference that many of our tests run against.

The general idea is that you can save yourself quite a bit of work (i.e. include way fewer configurations) by selectively allowing secondary lone phonons with some finite extent, instead of having to increase bare cloud size a lot.

[matthewcarbone]

Yep, others besides Mona have implemented it too. This really just boils down to modifying how we generate the original generalized_equations object.

[Chiffafox]

Agreed. I have personally done MA(1) by hand so far, and things get real hairy -- I can personally attest that I'd love an automated, GGCE-style approach to doing this.