Boson-Fermion Transmutation and the Statistics of Anyons

We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are analyzed. We show that the particle composite nature reduces the anti-bunching effect predicted for elementary bosons. Furthermore, the probability distribution exhibits a dispersion which is greater for composite bosons than for elementary b...

We review generalizations of quantum statistics, including parabose, parafermi, and quon statistics, but not including anyon statistics, which is special to two dimensions.

The formulae of boson powers commutation relation used by B. Sorensen [Nucl. Phys. A, v. 119, No 1, (1968), 65] in his calculations is erroneous. We provide the correct formulae.

The momentum operator representation of nonrelativistic anyons is developed in the Chern - Simons formulation of fractional statistics. The connection between anyons and the q-deformed bosonic algebra is established.

Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between Bose-Einstein and Fermi-Dirac statistics. The second quantization of Gentile statistics shows a lot of advantages. According to the symmetry requirement of the wave function, we give the general construction of transformation between anyon and Gentil...

In this paper we propose a unified statistics of Bose-Einstein and Fermi-Dirac statistics by suggesting that every particle can be associated with matter or fundamental forces with certain probability. The main Justification for this proposal is the possibility of extension of the spin-statistics theory to include a hypothesis quantum particles have fractional spin. The concept of Supersymmetry can be related to this unified statistics.

The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We establish that a q-deformed algebra can be used to describe the statistics of particles (anyons) interpolating continuously between Bose and Fermi statistics, i.e., fractional statistics. We show that the generalized intermediate statistics sp...

We propose the implementation of a switch of particle statistics with an embedding quantum simulator. By encoding both Bose-Einstein and Fermi-Dirac statistics into an enlarged Hilbert space, the statistics of quantum particles may be changed in situ during the time evolution, from bosons to fermions and from fermions to bosons, as many times as desired. We illustrate our proposal with few-qubit examples, although the protocol is straightforwardly extendable to larger numbers...

We show that it is possible to replace the actual implicit distribution function of the fractional exclusion statistics by an explicit one whose form does not change with the parameter $\alpha$. This alternative simpler distribution function given by a generalization of Pauli exclusion principle from the level of the maximal occupation number is not completely equivalent to the distributions obtained from the level of state number counting of the fractional exclusion particle...

I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and multiparticle interactions. The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories. Using an algebra of generalized functions, stat...