Anyon
Anyons (. Engl of any: any, not to be confused with anions) are exotic quasiparticles, the bosons ( integer spin ) fermions are not yet ( with half-integer spin). In the theoretical solid state physics, anyons are explored intensively in particular in connection with the quantum Hall effect. Recently, also experimental physicist and computer scientist deal with it, in the context of so-called " topological quantum computers."
Anyons can exist in only two dimensions, or as massless particles for mathematical reasons. As they are established in the two-dimensional quasi-particle systems (e.g., thin coatings).
The existence of the particles is a result of the fact that the type of quantum statistics of identical solid particles depends on the dimension of the space: the Hilbert space carries a unitary representation of the fundamental group of the configuration space. For one dimension this is the trivial group and there is no difference between fermions and bosons. For two dimensions, this is the Artin'sche " braid group " and for three dimensions and more the symmetric group. Since the braid group contains the symmetric group only as ratios, additional particle types are allowed in two-dimensional systems in addition to bosons and fermions.
For example, the fractional ( = fractional ) quantum Hall effect
The exchange of two elementary excitations with non-integer charge results here because of the attached magnetic flux quanta at 360 ° rotation to a Aharonov -Bohm phase, which neither π ( fermions ) is still 2π ( bosons ), but characterized by an arbitrary value θ
In connection with this effect, in particular the relationship with the integer and fractional quantum Hall effect, is also the concept of so-called " composite fermion " to date ( see below for references).
Applications
Applications include both real mathematical and abstract aspects such as the already mentioned Artin'sche braid group and currently speculative to be valued items such as a studied by experimental physicists and computer scientists promising " topological " realization of the (not yet existing! ) Quantum computer.