Evidence for Anyons, a Third Kingdom of Particles
quantamagazine.org
quantamagazine.org
Both are collective behaviors but most of the time you can think of protons as “balls made of quarks.” It’s not quite right but with semi classical treatment you get most of the effects. Anyons are not even approximately balls made of electrons. They break a lot of “classical particle” intuition the way protons don’t.
I wanted to highlight for a general reader that anyons are not particle in the sense of common intuition.
Protons, which the article brings as an example of collective phenomenona, roughly follow a lot of “particle intuition.”
Personally, I don’t mind if folks reify these things to make it easier to follow, fwiw.
That intuition is also most likely completely wrong.
Electrons in a material are effective particles, with a different mass, vide https://en.wikipedia.org/wiki/Effective_mass_(solid-state_ph....
Partice != fundamental particle.
For some weird reason, condensed matter physicists keep giving their quasiparticles the same names particle physicists give their particle particles, even though the mathematics are quite different. If you hear someone proclaiming the discovery of Majorana fermions, axions, or monopoles, it's essentially guaranteed to be a quasiparticle in a lump of metal or something. Sometimes even the articles themselves get confused about this.
Taking this further you might conclude that a soundwave isn't physical either. And sound is actually an examples of quasiparticles (phonons) when you get down to the quantum level.
Then again most people would be of the opinion that light propagates slower through solids like glass, but the photons in that description are quasiparticles (which have mass, unlike the photons in isolation). And quasiparticles share many properties that you'd normally expect only physical particles to have so it gets complicated.
Some elementary particles (quarks) don't really obey a lot of this intuition. Some none-elementary particles, for example protons/neutrons, do follow a lot of this intuition. Even some topological order quasiparticle in CMP follow this intuition -- magnetic skyrmions can be localized, can be imaged, have particle-like scattering.
Anyons don't follow this particle intuition.
In particular photons travelling through a medium are usually viewed as quasiparticles travelling slower than the speed of light, rather than a complex system of interactions. These particles have exactly the same kinds of behaviour as normal particles, similar to photons except with mass.
It might have been a good joke initially, but it should not have persisted as a scientific name.
The termination "-on" in the Ancient Greek words "electron" and "proton" does not have any concrete meaning, it is just the thematic vowel "o" followed by the marker "n", of a singular neuter noun (originally "m", but in Ancient Greek all final "m" became "n").
Combining some undeclinable English word with an Ancient Greek case termination seems ugly and pointless for me (not that "fermion" and "boson" are any better from this point of view).
Even if we accept making words to rhyme as a technique for coining new words, "anyon" remains a bad choice, because it is easily confused with "anion" (introduced by Faraday almost two hundred years ago).
I assume that "anyon" is meant to have a different pronunciation, i.e. like "any-on", but nonetheless, in almost all other languages the vowels are pronounced different than in English and the default pronunciation for "anyon" and "anion" will likely be the same.
The reference to Ancient Greek is a matter of taste, I prefer new words to either have a meaning or to have no meaning, i.e. to be random. I find words with nonsense meaning irritating and more difficult to remember.
At least "fermion" is just a distorted form of Fermi, which does not suggest any specific meaning.
On the other hand "any on", has a meaning, but a nonsensical one, i.e. its suggests a reference to any one of the "ons", but there is no such thing as an "on", as that is just a grammatical case marker.
By the way, the "-on" in "anion" is not the same as the "-on" in proton. While the "-on" in proton comes from "-om", the "-on" in anion comes from "-ont", which corresponds to the English "-ing", the suffix of the active participle (anion = upwards-going).
Now, there's nothing wrong with exploring those ideas and they might eventually be fruitful, but in terms of looking "further down" (which is typically the lure of the excitement), quasiparticles are only looking back up. I am of the mind that you could make assemblages of particles -- that is to say, quasiparticles -- do all kinds of oddball things that their constituents cannot. That is fine and often useful, but it isn't the further down we were interested in.
Does it mean "being moved on a circular path around something"? That would be simply a couple of translations, which change exactly nothing. Or does it happen in a sort of a field?
Taking the interpretation of "engulfing", like "a rope looped around a post engulfs it" shows a clear difference between 2D and 3D, and seems topologically relevant, but what does it mean "to go back again"?
Not knowing the topological model for particles beforehand, I am unable to learn anything from the article.
I can't exactly tell you how the topological part works but I can tell you that this statement isn't as simple as you think.
You're not reasoning about the location of a particle, but you should actually be reasoning about the Feynman path integral, the sum of all the probabilities of the potential paths that the particle could travel through in the future — because this is physics and our particles are all waves.
Say that translating the particle does not change its state. Imagine for a moment a macroscopic two dimensional system in which you have a globe depicting the Earth. Initially, this globe is set with the north pole facing up and the Greenwich meridian facing north. Draw an circle on the floor and place another sphere in the middle. Roll this globe around the circle. When you it returns to the initial location, does the globe look the same? It might not!
The globe has state and that state changes as it is moved around. Your globe changes direction because it is rotating on the floor. Particles don't have a floor to roll on, but they can have internal state.
If your globe ends up the same place after a circle, then your globe is a boson (phase factor 1). If the globe is upside down with Antarctica on top but otherwise the same, it is a fermion (phase factor -1). If Florida or the Ukraine or God-knows-what end up on top instead, it is an anyon.
Now, you're going to rig this up to a camera and do a time lapse (this is us taking the integral). Every time the globe passes the camera, take a photo. Stack all the photos after each other in a video. If you have a boson globe, any picture looks like one facet of the globe. If you have a fermion globe, you'll have a double-image, with "north" pointing two directions at once. If you have an anyon globe, well, it could look like a bunch of different things, and that's the point.
In physics, of course, we actually want to run this sort of integral on all sorts of circles simultaneously, instead of just one, and some of these circles are more probable than others, and everything gets all quantized (which is why the path integrals usually add up in a way that exclude anyons instead of that being the default.)
> Imagine two indistinguishable particles, like electrons. Take one, then loop it around the other so that it ends up back where it started. Nothing seems to have changed. And indeed, in the mathematical language of quantum mechanics, the two wave functions describing the initial and final states must be either equal or off by a factor of −1.
As explained later in the article, in three or more dimensions, if you loop a particle around another and back where it started, you did nothing at all. The factor is 1, not -1.
The actual thought experiment is that you swap two indistinguishable particles. The resulting state must be the same up to a scalar factor k, since, if it wasn’t, you could tell the particles apart. Moreover, if you swap two particles twice, you end up exactly where you started, so k^2=1.
In two dimensions, this all breaks down a bit, and it gets very complicated very quickly.
f(x0, x1)
where x0 and x1 are coordinates of the two particles.
The fact that the particles are indistinguishable means that no possible experiment can tell them apart. After a bit of math, this means that f(x0, x1) = k * f(x1, x0) where k is a constant. All wavefunctions are normalized, so |k|^2=1, which constrains k to be on the unit circle.
But you can go farther: it's possible, at least in principle, to come up with an experiment that measures k. So you start with the particles in their initial state, do your experiment, and learn k. (Maybe you need to repeat it a bunch of times -- no big deal.) Now you repeat the same experiment but start with the two particles having their roles swapped. Since the particles are indistinguishable, you had better measure the same value for k. This means:
f(x0, x1) = k * f(x1, x0)
and also
f(x1, x0) = k * f(x0, x1) = k^2 * f(x1, x0)
So k^2 = 1, and that rules out everything except k=1 or k=-1.
There are two distinct things going on here: formally "swapping" the arguments in the wavefunction, and physically moving the particles around. A priori, there is no reason the phase shifts from these two actions should be related.
You're focusing on the swap, but it's not interesting: your argument that the swap phase squares to 1 applies to both 2D and 3D equally well. When people talk about anyons, they're talking about the phase from moving the particles. That has more options in 2D because the paths one can take when moving particles around can have a greater range of topologies (https://en.wikipedia.org/wiki/Braid_group).
The reason that textbooks mix these things up is because in relativistic quantum field theories these two phases are always the same, by virtue of the spin-statistics theorem. But the anyons of condensed matter are nonrelativistic.
> To understand the quantum kingdoms, think of a drawing of loops. Imagine two indistinguishable particles, like electrons. Take one, then loop it around the other so that it ends up back where it started. Nothing seems to have changed. And indeed, in the mathematical language of quantum mechanics, the two wave functions describing the initial and final states must be either equal or off by a factor of −1. ... If the wave functions are identical, your quantum particles are bosons. If they’re off by a factor of −1, you have fermions.
This is nonsense. In 3D, you can't even define what it means to loop one particle around another, and there is nothing at all that says that fermions behave in a particular way when you loop them around some other particle.