[Jarek Duda (OP)]

Especially in superconductors/superfluids there are observed so called macroscopic quantum phenomena ( https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena ) - stable constructs like fluxon/Abrikosov vortex quantizing magnetic field due to toplogical constraints.
There is observed e.g. interference ( https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.094503 ), tunneling ( https://journals.aps.org/prb/pdf/10.1103/PhysRevB.56.14677 ), Aharonov-Bohm (https://www.sciencedirect.com/science/article/pii/S0375960197003356  ) effects for these particle-like objects.

It brings question if this similarity with particle physics could be taken further? How far?
E.g. there is this famous Volovik's "The universe in helium droplet" book ( http://www.issp.ac.ru/ebooks/books/open/The_Universe_in_a_Helium_Droplet.pdf ).
Maybe let us discuss it here - any interesting approaches?

For example there are these biaxial nematic liquid crystals: of molecules with 3 distinguishable axes.
We could build hedgehog configuration (topological charge) with one these 3 axes, additionally requiring magnetic-like singularity for second axis due to hairy-ball theorem ... doesn't it resemble 3 leptons: asymptotically the same charge (+magnetic dipole), but with different realization/mass?

[Jarek Duda (OP)]

Let me take a bit further this analogy (can much further) - in superfluid biaxial nematic we would also need 1D fluxon-like configuration - along one of 3 distinguishable axes.
Such fluxons can e.g. form a short loop of one of 3 types - which should have much lower mass/energy than charge, be stable and extremely difficult to interact with, can transform between 3 types with internal rotation ... don't they resemble 3 neutrinos and https://en.wikipedia.org/wiki/Neutrino_oscillation ?

[yor_on]

That was a interesting pdf Jarek. It will take me some time to read it though.

[Jarek Duda (OP)]

There is a growing society of physicists going in this direction, e.g. here are lots of interesting talks for example toward such models of nuclei: http://solitonsatwork.net/?display=archive
Basic book: http://www.lmpt.univ-tours.fr/~volkov/Manton-Sutcliffe.pdf
Some recent liquid crystal experimental paper: https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-8-2-255&id=447762

Models of nuclei from https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.232002


ps. Nice mechanical realization of 1D topological solitons - both moving and traveling, with pair creation/annihilation:

[Jarek Duda (OP)]

Very nice paper with observed particle-like topological configurations in liquid crystal:

"Annihilation dynamics of topological defects induced by microparticles in nematic liquid crystals": https://pubs.rsc.org/en/content/articlelanding/2019/sm/c9sm01710k#!divAbstract

There is also long-range interaction: F ~ charge1*charge2/D Coulomb-like formula (1.2) below:



ps. This discussion has developed in https://www.scienceforums.net/topic/124416-similarity-between-particle-physics-and-macroscopic-quantum-phenomena-like-fluxons/

[Jarek Duda (OP)]

There are more long-range interactions for topological solitons in liquid crystals, e.g.:
- Coulomb: "Coulomb-like interaction in nematic emulsions induced by external torques exerted on the colloids" https://journals.aps.org/pre/abstract/10.1103/PhysRevE.76.011707
- dipole-dipole: "Novel Colloidal Interactions in Anisotropic Fluids" https://science.sciencemag.org/content/275/5307/1770
- quardupole-quadrupole: "Long-range forces and aggregation of colloid particles in a nematic liquid crystal": https://journals.aps.org/pre/abstract/10.1103/PhysRevE.55.2958



Skyrme models are for strong interaction ... so why can't we model all?

These liquid crystal systems are for uniaxial nematic - one distinguished axis everywhere ... bringing a question about natural generalization: biaxial nematic: 3 distinguished axes in 3D (4 in spacetime adds gravity) - giving particle-like configurations resembling 3 leptons, neutrinos, baryons, nuclei ...