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Anyon
In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect.
The statistical mechanics of large many-body systems obeys laws described by Maxwell–Boltzmann statistics. Quantum statistics is more complicated because of the different behaviors of two different kinds of particles called fermions and bosons. In two-dimensional systems, however, there is a third type of particle, called an anyon.
In the three-dimensional world we live in, there are only two types of particles: "fermions", which repel each other, and "bosons", which like to stick together. A commonly known fermion is the electron, which transports electricity; and a commonly known boson is the photon, which carries light. In the two-dimensional world, however, there is another type of particle, the anyon, which doesn't behave like either a fermion or a boson.
— "Finally, anyons reveal their exotic quantum properties", Aalto University press release, April 2020
In a two-dimensional world, two identical anyons change their wavefunction when they swap places in ways that cannot happen in three-dimensional physics:
...in two dimensions, exchanging identical particles twice is not equivalent to leaving them alone. The particles' wavefunction after swapping places twice may differ from the original one; particles with such unusual exchange statistics are known as anyons. By contrast, in three dimensions, exchanging particles twice cannot change their wavefunction, leaving us with only two possibilities: bosons, whose wavefunction remains the same even after a single exchange, and fermions, whose exchange only changes the sign of their wavefunction.
— Kirill Shtengel, "A home for anyon?", Nature Physics
This process of exchanging identical particles, or of circling one particle around another, is referred to as "braiding". Braiding two anyons creates a historical record of the event, as their changed wave functions record the number of braids.
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Anyon
In physics, an anyon is a type of quasiparticle so far observed only in two-dimensional systems. In three-dimensional systems, only two kinds of elementary particles are seen: fermions and bosons. Anyons have statistical properties intermediate between fermions and bosons. In general, the operation of exchanging two identical particles, although it may cause a global phase shift, cannot affect observables. Anyons are generally classified as abelian or non-abelian. Abelian anyons, detected by two experiments in 2020, play a major role in the fractional quantum Hall effect.
The statistical mechanics of large many-body systems obeys laws described by Maxwell–Boltzmann statistics. Quantum statistics is more complicated because of the different behaviors of two different kinds of particles called fermions and bosons. In two-dimensional systems, however, there is a third type of particle, called an anyon.
In the three-dimensional world we live in, there are only two types of particles: "fermions", which repel each other, and "bosons", which like to stick together. A commonly known fermion is the electron, which transports electricity; and a commonly known boson is the photon, which carries light. In the two-dimensional world, however, there is another type of particle, the anyon, which doesn't behave like either a fermion or a boson.
— "Finally, anyons reveal their exotic quantum properties", Aalto University press release, April 2020
In a two-dimensional world, two identical anyons change their wavefunction when they swap places in ways that cannot happen in three-dimensional physics:
...in two dimensions, exchanging identical particles twice is not equivalent to leaving them alone. The particles' wavefunction after swapping places twice may differ from the original one; particles with such unusual exchange statistics are known as anyons. By contrast, in three dimensions, exchanging particles twice cannot change their wavefunction, leaving us with only two possibilities: bosons, whose wavefunction remains the same even after a single exchange, and fermions, whose exchange only changes the sign of their wavefunction.
— Kirill Shtengel, "A home for anyon?", Nature Physics
This process of exchanging identical particles, or of circling one particle around another, is referred to as "braiding". Braiding two anyons creates a historical record of the event, as their changed wave functions record the number of braids.