Statistical mechanics of anyons

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as Nfold braided-symmetric tensor products of the 1-particle Hilbert space. This perspective provides a convenient Fock space construction for nonrelativistic anyon quantum fields along the more usual lines of boson and fermion fields, but in a braided category, and clarifies how discrete (lattice) anyon fields relate to anyon fields in the continuum. We also see how essential physical information is encoded. In particular, we show how the algebraic structure of the anyonic Fock space leads to a natural anyonic exclusion principle related to intermediate occupation number statistics, and obtain the partition function for an idealized gas of fixed anyonic vortices.

show abstract

“…From the partition function one may then proceed as usual to thermodynamic properties of such a gas [31].…”

Section: Roots Of Unity and The Anyonic Exclusion Principlementioning

confidence: 99%

On the Fock space for nonrelativistic anyon fields and braided tensor products

Goldin

Majid

2004

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Interesting results have also been derived to describe the thermostatistics of anyons, such as determining the virial coefficients [11,13]. However, the theoretical basis of the statistical mechanics of anyons has not really been established.…”

Section: Introductionmentioning

confidence: 99%

Detailed balance and intermediate statistics

Acharya

Swamy

2004

J. Phys. A: Math. Gen.

Self Cite

View full text Add to dashboard Cite

We present a theory of particles, obeying intermediate statistics ("anyons"), interpolating between Bosons and Fermions, based on the principle of Detailed Balance. It is demonstrated that the scattering probabilities of identical particles can be expressed in terms of the basic numbers, which arise naturally and logically in this theory. A transcendental equation determining the distribution function of anyons is obtained in terms of the statistics parameter, whose limiting values 0 and 1 correspond to Bosons and Fermions respectively. The distribution function is determined as a power series involving the Boltzmann factor and the statistics parameter and we also express the distribution function as an infinite continued fraction. The last form enables one to develop approximate forms for the distribution function, with the first approximant agreeing with our earlier investigation.

show abstract

“…We find another interesting proposal for generalizing Bose-Einstein and Fermi-Dirac statistics in (9), where the distribution function for the number of anyons in a given state j is postulated at once as…”

Section: Quons Anyons and Generalized Statisticsmentioning

confidence: 99%

Quantum Statistics and Coherent Access Hypothesis

Almeida¹

2012

Some Applications of Quantum Mechanics

View full text Add to dashboard Cite

Statistical mechanics of anyons

Cited by 48 publications

References 19 publications

On the Fock space for nonrelativistic anyon fields and braided tensor products

On the Fock space for nonrelativistic anyon fields and braided tensor products

Detailed balance and intermediate statistics

Quantum Statistics and Coherent Access Hypothesis

Contact Info

Product

Resources

About