Hello Eric, Tensors and Hamiltonians? Oh dear, reminds me of Bessel functions to model vinyl deformation. I’ll chime in to say that I am very interested -– actually excited! – about the possibility of your returning to the cartridge design world. So I'll offer a few musings.
Experiments re modeling phono pickups has convinced me that achieving flat frequency response is easy. Achieving low mechanical impedance (to allow low VTFs for reasons of record wear and vinyl deformation loss) is also easy. But to achieve both goals concurrently is extremely challenging.
I’ve long been a fan of various top ADC and Shure models (and Paul Weather’s designs before then). The later models in these lines started to demonstrate that low mechanical impedance AND extended flat FR can be achieved concurrently. Unfortunately the goal of low mechanical impedance has been largely abandoned, both for new pickups and replacement styli. Absurdly expensive MCs are the current darlings.
It seems to me that MI/MM technology is more amenable to these goals than is MC. (a.) They are simpler mechanically and probably easier to manufacture. (b.) Having a user-replaceable stylus should be a must. (c.) Tayloring the MI/MM source/load impedance electrical response against the stylus mechanical response is a useful tool to tame the inevitable HF resonance peaks. Low-Z MCs can’t do this, and thus need to heavily mechanically damp the stylus to tame the HF peak – thus leading to today’s overdamped MCs with low compliance, heavier VTF, and the popularity of heavier arms. (d.) A side issue with Low-Z pickups (not having electrical HF rolloff) is that their response above the audio range introduces unwanted ultrasonic input to the associated preamp, leading to potential overload which can affect the audio range signal. (e.) Probably stronger modern magnets can allow coil structures with lower source impedance. (f.) Perhaps also provide greater eddy current damping of the stylus.
So … I see a need for an updated version of the ADC XLM, Astrion, Shure V15V, et al. Probably with a single prescribed VTF (not a range) so that the generator geometry is defined. But are there current compatible arms? Perhaps a matching arm integrated with the cartridge, is the answer. That way the designer has fuller control. (Yep, we’ve been there, done that. Didn’t sell. But still valid.)