Easily specify parameters for various limits

[evanberkowitz]

We should have simple ways to specify the various parameters that go into the code.

The code requires the dimensionless

• ~β = β/ML^2,
• ~μ = ML^2 µ,
• ~h = ML^2 h,
• ~a = 2π a / L and Nt and Nx control only discretization effects (not finite-volume physics). So, a single finite-volume computation needs all four ~parameters set, plus a specification of a spacetime lattice.

In the infinite-volume (L-->∞) finite-temperature thermodynamic limit then we need to specify three dimensionless ratios

• One of βμ = ~β~μ, log z, z
• One of βh = ~β~h, log zh, zh
• One of βε(binding), λdB/a, ~β/~a^2. and to get finite-volume parameters we need to provide one of ~β, ~μ, (or ~h, so long as it is proportional to βh).

To take a thermodynamic limit, presumably you want to

1. Specify the thermodynamic parameters
2. Provide one more parameter to get finite-volume parameters.
3. Repeat for different values of the last parameter to head towards the infinite-volume limit.

Question: how to get the thermodynamic parameters?

Some experiments quote results already in dimensionless figures. See, for example, Boettcher et al., Phys. Rev. Lett. 116, 045303 (2016), where the EOS is given in terms of βμ and βε.

But others provide dimensionful parameters. They might say something like

• [the external field is 0; I don't know their preferred unit for h]
• M is (the mass of 6Li)
• a is tuned to (foo µm)
• µ is (bar nK),
• T is (baz nK),
• L is (quux µm) which (given the dynamics / EOS) gives a number density of n = 2/µm^2. Given the first 5 of these we can calculate the three dimensionless thermodynamic ratios. Given L we can get the finite-volume parameters.

All of this assumes the scattering is completely described by a scattering length and nothing else. So it's not completely generic. However it is likely a common enough use case that we should probably incorporate it directly into tdg, rather than store it in some paper's repo. Then, the question: what should we call this submodule?

[evanberkowitz]

Some options

• tdg.leading_order
• tdg.LO (in anticipation of NLO, etc.)
• tdg.parameters (ultimately just replace a with an ERE)