Similarity between particle physics and macroscopic quantum phenomena like fluxons?

J

Jarek Duda

Registered Senior Member
Especially in superconductors/superfluids there are observed so called macroscopic quantum phenomena ( https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena ) - stable configurations like fluxon/Abrikosov vortex quantizing magnetic field due to topological constraints (phase change along loop has to be multiplicity of 2pi).
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? ( https://arxiv.org/pdf/2108.12359 )
kKLhvUV.png
 
Thanks for pointing https://en.wikipedia.org/wiki/Koide_formula - very interesting, suggesting a result of some e.g. geometric optimization, I will have it in mind.

Generally, while QFT sees electron as just "result of electron creation operator", it is quite complex field configurations: charge, magnetic dipole, angular momentum ... and also ~10^21 Hz de Broglie clock/zitterbewegung (intrinsic periodic process, confirmed experimentally: https://link.springer.com/article/10.1007/s10701-008-9225-1 ) - it would be great to finally understand these field configurations ...

obraz.png
 
Thanks, regarding spin, it is related with magnetic dipole moment of particle.
There are known fluxons ( https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena ) - 2D topological charges carrying quant of magnetic field.
Quantum rotation operator says: rotating spin s by phi angle, phase changes by phi * s.

All of these perspectives agree with vortexes of given 2D topological charge - so I interpret it as spin.
Also, if object rotated by pi is the same object (e.g. ellipsoid), we can get spin 1/2 this way:

obraz.png
 
Jarek Duda said:
Thanks, regarding spin, it is related with magnetic dipole moment of particle.
There are known fluxons ( https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena ) - 2D topological charges carrying quant of magnetic field.
Quantum rotation operator says: rotating spin s by phi angle, phase changes by phi * s.

All of these perspectives agree with vortexes of given 2D topological charge - so I interpret it as spin.
Also, if object rotated by pi is the same object (e.g. ellipsoid), we can get spin 1/2 this way:

obraz.png
Click to expand...
Gsponer's final comment on the nature of particle spin:

"Finally, it is clear that “spin” has nothing to do with a vortex or a whirl which would be carried by a wave or a wave-packet: It is simply the non-local part of the angular momentum that derives from the dynamics implied by the wave-equations defining the field."

Which is at odds with your condensed matter analog perspective.

The strange to me thing is his expression for normalized spin density eqn (1) should be precisely zero given what he subsequently writes:

"This means that the definition (1) is consistent with Maxwell’s equations and the notion of a wavepacket if E = −∂A/∂t, that is, only if the scalar potential is such that ∇φ = 0."

What am I missing, or is Gsponer pulling off an elaborate April Fools day joke?

Upon further reflection.....I get it now. For a photon propagating at c as wavepacket, there is not just a changing amplitude for A, but rotation as well. It's exclusively the latter that yields a nonzero E × A. So not an April Fools day joke.
 
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Maybe Gsponer has meant that spin of e.g. electron is not exactly spinning, what I agree.
Topological charge is kind of "structural spinning" - what is a bit different than actual spinning like a tornado.
It is just agreeing with quantum rotation operator: rotating spin s objects phi angle, rotates spin by s*psi.
 
Thanks for pointing https://arxiv.org/pdf/1806.01121.pdf
Spin is not only about spinning, but also for quantum rotation operator: "rotating spin s particle by phi angle, phase rotates by phi*s" - what needs topological charge like above, or in fluxons.

The main point here is repairing electromagnetism:
1) that Gauss law can give any real charge, while in nature only integer - repaired by interpreting field curvature as electric field, what makes Gauss law count topological charge - which is quantized.
2) Infinite energy of electric field of point charge - repaired by using Higgs-like potential, allowing for deformation of EM to prevent such singularities (regularization).
 
Jarek Duda said:
Thanks for pointing https://arxiv.org/pdf/1806.01121.pdf
Spin is not only about spinning, but also for quantum rotation operator: "rotating spin s particle by phi angle, phase rotates by phi*s" - what needs topological charge like above, or in fluxons.

The main point here is repairing electromagnetism:
1) that Gauss law can give any real charge, while in nature only integer - repaired by interpreting field curvature as electric field, what makes Gauss law count topological charge - which is quantized.
2) Infinite energy of electric field of point charge - repaired by using Higgs-like potential, allowing for deformation of EM to prevent such singularities (regularization).
Click to expand...

I admit, that this is beyond my very limited particle physics knowledge, but lets imagine, you are right in both points. And what? Would be there some major modification to some major theories? Or even some potential technological application?
 
The main point is repairing electromagnetism - add missing charge quantization, and regularize charges to finite energy.
However, adding missing charge quantization, the simplest nontrivial charge becomes model of leptons ...

The big question is if could get more particles?
Nice talk about observed particle-like in liquid crystals

Looking at biaxial nematic, its topological defects start resembling particle physics menagerie - maybe it is a coincidence(?), but maybe it could lead to better understanding of particle physics: with concrete e.g. EM field configurations.
 
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