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Similarity between particle physics and macroscopic quantum phenomena like fluxons?


Duda Jarek
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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 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?

kKLhvUV.png

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In any case, here are lots of interesting talks e.g. 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

SkyrmionsWithRho.jpg

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Sure solitons can travel (e.g. getting Lorentz contraction), also nuclei (especially in LHC) - ideally we would like to recreate the space of possible particle, including their dynamics.

For example we can recreate Coulomb interaction/Maxwell equations between topological charges: defining curvature of field of e.g. unitary vectors as EM field, Gauss law counts winding number/topological charge. Then using standard EM Lagrangian for this curvature leads to Maxwell equations - with built in charge quantization as topological (Faber's model https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012022/pdf )

The question is how far we can go this way - which particles can be modeled as such "macroscopic quantum phenomena"?

 

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

 

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49 minutes ago, Duda Jarek said:

Sure solitons can travel

Can travel ?

Not sure you understand what a soliton is.

They are are a particular phenomenon that can occur in travelling waves ie they are never still.

I know that there are soliton models of photons (which are never still) in modern Optics.

Hence my question.

 

I recommend this book as an introduction

drazin1.jpg.7ab04bf72a0504de2f7459f1a523de98.jpg

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I am interested in solitons models of particles for more than a decade, some slides: https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf

As particles, topological solitons can stay in place or travel - getting SR effects while approaching propagation speed, like Lorentz contraction, time dilation (e.g. for breathers), mass/momentum scaling.

For example resting and traveling kink of this mechanical realization of sine-Gordon model:

obraz.png.ef8e6cf3c8bc4405d8d07aa3d3405b81.png

Edited by Duda Jarek
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1 hour ago, Duda Jarek said:

I am interested in solitons models of particles for more than a decade, some slides: https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf

As particles, topological solitons can stay in place or travel - getting SR effects while approaching propagation speed, like Lorentz contraction, time dilation (e.g. for breathers), mass/momentum scaling.

 

 

Truly amazing, what will they think of to redefine next ?  +1

I had not heard of 'topological solitons' , which are quite different phenomena from solitons.

I se there is a Wiki article about them

https://en.wikipedia.org/wiki/Topological_defect

 

You will need to hope that someone else here has met them to discuss them as it will take me some time to catch up.

But I will watch the development of this thread with interest.

Thank you for introducing the subject.

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Posted (edited)

Maybe let me briefly elaborate how I would hope to get all the particles from the biaxial nematic-like field (?), would gladly discuss:

1) we get 3 hedgehog realizations of one of 3 axes - kind of 3 leptons (the same charge, different energy/mass), with magnetic dipole due to the hairy ball theorem, Faber's approach ( https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012022/pdf ) gives Coulomb interaction for them,

2) the simplest vortex loop resembles neutrino: stable - very difficult to interact with, 3 types: along one of 3 axes, can "oscillate" between them by internal rotation, are produced in beta decay,

3) loop with internal twist (hopfions?) might correspond to mesons, number of twists nicely fits strangeness - agrees with decay of mesons, strange baryons ( https://en.wikipedia.org/wiki/List_of_baryons ),

4) if another vortex goes through such loop, it nicely resembles baryons, interaction between its vortices creates charge inside (diagram below). Proton just closes this charge, while neutron has to compensate it - what is costly, explaining why neutron is heavier than proton (also quark-like fractional charge distribution),

5) combining baryons form nuclei as various size knots - binding them against Coulomb repulsion, including halo neutrons binded in much larger distance ( https://en.wikipedia.org/wiki/Halo_nucleus )

7GmZbZs.png

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On 2/26/2021 at 4:56 PM, studiot said:

I had not heard of 'topological solitons' , which are quite different phenomena from solitons.

The terminology has changed quite a bit over the years. Look at this for an appetiser:

https://en.wikipedia.org/wiki/Soliton_(disambiguation)

(I think there are more.)

The bone of contention to me is: What about quantum mechanics? Bell-Clauser-Horne-Shimony, Bell-Kochen-Specker and Greenberger-Horne-Zeilinger-Mermin theorems --and their experimental confirmations-- tell us that it is not consistent to assume on the basis of classical logic alone a particular orientation of the particle.

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Posted (edited)

The basic definition of soliton from https://en.wikipedia.org/wiki/Soliton is "In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity."

For example with electron there comes E ~ 1/r^2 electric field, "while it propagates at a constant velocity" - doesn't it make electron formally a solitons?

What more e.g. electron is than "sum of its fields"?

Let me quote Einstein again from 1961 Infeld "Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta.":

Pwy6aXi.png

Regarding quantum effects for solitons, many are observed e.g. in superconductors/superfluids - I have started this thread with:

On 2/19/2021 at 6:53 AM, Duda Jarek said:

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 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.

There are also observed hydrodynamical analogues of many quantum phenomena, like Casimir, Aharonov-Bohm, orbit quantization etc. - gathered lots of papers: https://www.dropbox.com/s/kxvvhj0cnl1iqxr/Couder.pdf

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11 minutes ago, Duda Jarek said:

The basic definition of soliton from https://en.wikipedia.org/wiki/Soliton is "In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity."

 

Thank you.

So you now agree that a soliton cannot stand still as I originally said ?

 

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Posted (edited)

The "constant velocity" can be just v=0 ... especially that these are usually Lorentz-invariant models: allowing to change frame of reference to make the constant velocity zero. In this case, massive solitons scale mass/momentum exactly as in special relativity - they go to infinity while approaching propagation speed.

See the sine-Gordon mentioned a few times, realized mechanically, or similar phi^4 - here is resting kink from https://en.wikipedia.org/wiki/Topological_defect#Images

DoubleWellSoliton.png

Here are initially two opposite topological charges traveling with constant velocities, which meet and annihilate - releasing mass (energy) as massless radiation (usually traveling at maximal - propagation speed):

DoubleWellSolitonAntisoliton.gif

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9 minutes ago, Duda Jarek said:

The "constant velocity" can be just v=0 ..

You have to demonstrate this, not just claim it.

 

As far as I understand the 'internal' mechanism of a soliton is such that it has to be in continual motion for the 'self - reinforcing' mechanism to operate.
(That was also in your quote.)

The only way such an entity can be 'stationary' is if the medium is moving in the opposite direction at the same speed as the soliton.

You also introduced vortices.
Vortex phenomena are different in that they can stand still. You can observe this in ordinary stream flow in a river bed where there are permanent eddies.

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Posted (edited)

See e.g. the mechanical realizations of sine-Gordon - lattice of pendulums connected by a spring. Rotating them from one side, you get v=0 kink - going from one minimum of potential to the next one: rotated by 2pi.

obraz.png

Here on slide 11 you have derived formulas, mass/momentum scaling as in SR: https://www.dropbox.com/s/aj6tu93n04rcgra/soliton.pdf

obraz.png.d016a1b69d62e70881abaaa674aea771.png

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So you have a bunch of unexplained mathematics, including a velocity term that tends to unity (1) and a couple of graphs with their axes not labelled.

How does this demonstrate that a soliton is standing still ?

Are you not not confusing a stationary state in a plot with an entity standing still ?

Edited by studiot
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3 minutes ago, Duda Jarek said:

But I have also sent you video of somebody's demonstration (e.g. https://www.youtube.com/watch?v=nl5Qq5kUbEE ) ... sine-Gordon is an old well established model: with varying number also of massive particles, behaving exactly as in special relativity ... in looking trivial model - just: phi_tt = phi_xx - sin(phi).

I can't watch the video at the moment and it is , as you say, someone else's model.

This is your thread so you should be offering your supporting development, not just copy/pasting other people's work.

 

Do you understand the hydraulic jump ?

The hydraulic jump behaves in a very similar way to the graph you showed.

The jump is 'stationary' in that it always occurs in the same place for a fixed geometry.

It builds up, rather like the sequence of coloured curves in your top sigmoid plot, at a fixed point on the horizontal axis, until there is a macroscopic 'quantum jump' in the water surface.

But the water has to be flowing.

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This thread was supposed to be general as in title - about "Similarity between particle physics and macroscopic quantum phenomena like fluxons?" ... and sine-Gordon is just one of well established basic toymodels here.

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56 minutes ago, Duda Jarek said:

This thread was supposed to be general as in title - about "Similarity between particle physics and macroscopic quantum phenomena like fluxons?" ... and sine-Gordon is just one of well established basic toymodels here.

A 3-D soliton, micro (atomic level ) or macro (a tsunami) , may be planned on a 2-D plane with incoherent spatial intensity distributions. All The external control offers great experimental possibilities to control the lateral orientation of the feedback solitons both statically and dynamically. These instabilities play a crucial role in determining soliton existence's static and dynamic circumstances.

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On 2/26/2021 at 1:30 PM, Duda Jarek said:

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

 

1 hour ago, Duda Jarek said:

This thread was supposed to be general as in title - about "Similarity between particle physics and macroscopic quantum phenomena like fluxons?" ... and sine-Gordon is just one of well established basic toymodels here.

 

Both "moving and travelling"  your own words about the video you linked to.

 

I have now had the opportunity to watch this video and have a couple of comments.

1) As a demonstration it is interesting but you need to be able to explain (not just state) what it demonstrates.

2) There is a mistake in the presenter's script at about 2 and a half minutes.

He says " the pendulums fly out further and further as the rotation speed increases"

The bobs appear to be suspended on rigid rods so how is this possible ?

3) Yes The mechanism does show a wave travelling along the length of the shaft, being reflected at the far end and travelling back.

Two waves not one.

Yes: These two waves interfere to produce a standing wave, non linear but conventional. These are not solitons.

 

According to my understanding the following definitons apply.

For a given waveshape, the speed of propagation of a nonlinear wave depends upon its amplitude.
Larger amplitude waves of the same shape travel faster than smaller amplitude waves.

If the waveshape of a single nonlinear travelling pulse does not change as it propagates, it is called a (travelling) solitary wave.

A travelling solitary wave can interfere with another wave of the same shape but going the other way to produce a standing solitary wave.

But also and unlike linear waves, that all travel at the same speed, nonlinear waves of the same shape but different amplitudes have additional posiible modes of

interaction.

The larger amplitude and therefore faster,  non linear wave, can overtake another nonlinear wave.
When it catches the first smaller wave, there is a time of complicated interaction.
If the two waves finally emerge as before, they are called solitons.
Not all nonlinear waves have this property of the faster wave being able to 'pass through' the slower one.

 

Now you did not answer my question about the hydraulic jump.

Your title is about macroscopic phenomena and I was trying to help you with physical understanding using this macroscopic phenomenon.

 

From what I can make out, such waves can occur in a phase space rather than physical space.
So we need to distinguish clearly between the physical and the model representation.

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The way Studiot propounds stipulations and modalities, then such waves can occur ONLY in a phase space rather than in physical space. 

What is the probability of actually finding out any physicalistic merger of waves if they are to be still named "Solitons" ?

 

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1 hour ago, Prof Reza Sanaye said:

The way Studiot propounds stipulations and modalities, then such waves can occur ONLY in a phase space rather than in physical space. 

What is the probability of actually finding out any physicalistic merger of waves if they are to be still named "Solitons" ?

 

The first physical solitons were reported by the first man to investigate such phenomena

Russell J S  Report on Waves Rep. 14the Meet.Brit.Adv.Sci.,York,311-90. 1884

He also uncovered another interesting interaction property of non linear waves.

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20 minutes ago, studiot said:

The first physical solitons were reported by the first man to investigate such phenomena

Russell J S  Report on Waves Rep. 14the Meet.Brit.Adv.Sci.,York,311-90. 1884

He also uncovered another interesting interaction property of non linear waves.

So therefore , let us not limit them into phase spaces . . . .

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