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Related to Anyons: Fractional statistics


Particles obeying unconventional forms of quantum statistics. For many years it was believed that only two possible forms of quantum statistics, Bose-Einstein and Fermi-Dirac statistics, were possible, but in fact a continuum of possibilities exists. Elementary excitations (quasiparticles) in the fractional quantum Hall effect are anyons.

In quantum mechanics, in the behavior of identical particles there are important dynamical effects that have no classical analog. Thus, in the case of two indistinguishable particles A and B, the amplitude for the process that leads to A arriving at point x while B arrives at point y must be added to the amplitude for the process that leads to A arriving at y while B arrives at x—the so-called exchange process—because the final states cannot be distinguished. Actually the recipe of adding the amplitude for the exchange process is appropriate only for particles obeying Bose-Einstein statistics (bosons); for particles obeying Fermi-Dirac statistics (fermions), this amplitude must be subtracted. See Fermi-Dirac statistics

The definition of anyons posits other possible recipes for adding exchange processes, refining the analysis of exchange to take account of the direction in which the exchange takes place. These more general possibilities can be defined only for particles whose motion is restricted to two space dimensions. However, many important materials are effectively two-dimensional, including microelectronic circuitry and the copper oxide layers of high-temperature superconductors. The quantum statistics of the quasiparticles in these systems is under investigation, but the fractional quantized Hall states are known to be anyons. See Hall effect, Quantum statistics, Superconductivity

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References in periodicals archive ?
Anyons are generally classified as abelian or non-Abelian.
Non-Abelian anyons are those that can retain memory of their past states.
When this happens, we can eject anyons as "quasiparticles" from the correlated states of many electrons in the sheet.
The team plans on looking into the quantum Hall effect to help identify non-Abelian anyons.
In fractional quantum Hall states - a type of collective electron state observed only in two dimensional samples at very high magnetic fields - the quasiparticles are known to have precisely a rational fraction of the electron charge, implying that they are anyons," Young said in the release.
These anyons can only be studied when these materials are at exceptionally low temperatures and this makes it difficult to explore the unique quantum properties of individual anyons in this temperature.
Anyons come in a variety of types, and if two different anyons bump into each other, they either annihilate each other or fuse into a single particle.
What's more, different braids lead to different transformations, so one can figure out something about the particular braid the anyons traversed by measuring what happens when the anyons collide.
Nonabelian anyons are not obscure mathematically--they're rather simple, and there's no overriding physical law that has to be broken to make them," he says.
He has teamed up with Freedman to explore the possibility of creating nonabelian anyons in systems consisting of many thin layers of magnets.