• Corpus ID: 221970172

Exchange and exclusion in the non-abelian anyon gas

  title={Exchange and exclusion in the non-abelian anyon gas},
  author={Douglas Lundholm and Viktor Qvarfordt},
  journal={arXiv: Mathematical Physics},
We review and develop the many-body spectral theory of ideal anyons, i.e. identical quantum particles in the plane whose exchange rules are governed by unitary representations of the braid group on $N$ strands. Allowing for arbitrary rank (dependent on $N$) and non-abelian representations, and letting $N \to \infty$, this defines the ideal non-abelian many-anyon gas. We compute exchange operators and phases for a common and wide class of representations defined by fusion algebras, including the… 

A Lieb–Thirring inequality for extended anyons

We derive a Pauli exclusion principle for extended fermion-based anyons of any positive radius and any nontrivial statistics parameter. That is, we consider 2D fermionic particles coupled to magnetic

Magnetic perturbations of anyonic and Aharonov–Bohm Schrödinger operators

We study the Hamiltonian describing two anyons moving in a plane in presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding

Direct methods to Lieb-Thirring kinetic inequalities

We review some recent progress on Lieb-Thirring inequalities, focusing on direct methods to kinetic estimates for orthonormal functions and applications for many-body quantum systems.

Properties of 2D anyon gas

An overview is given of the 2D many-anyon gas, including its definition (both for ideal and certain less-than-ideal particles, as well as for abelian and nonabelian braid group representations), its

Anyons in a tight wave-guide and the Tonks-Girardeau gas

We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter \alpha \in ]0,2[. In the magnetic gauge picture they are described as bosons attached to



A Short Introduction to Fibonacci Anyon Models

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse

Hardy and Lieb-Thirring Inequalities for Anyons

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $${\alpha \in [0, 1]}$$α∈[0,1] ranging from bosons

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

We realize the physical N-anyon Hilbert spaces, introduced previously via unitary representations of the group of diffeomorphisms of the plane, as N-fold braided-symmetric tensor products of the

Degeneracy Implies Non-abelian Statistics

A non-abelian anyon can only occur in the presence of ground state degeneracy in the plane. It is conceivable that for some strange anyon with quantum dimension $>1$ that the resulting

Statistical interparticle potential of an ideal gas of non-Abelian anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern–Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of

Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states

We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level,