# Exchange and exclusion in the non-abelian anyon gas

@article{Lundholm2020ExchangeAE, title={Exchange and exclusion in the non-abelian anyon gas}, author={Douglas Lundholm and Viktor Qvarfordt}, journal={arXiv: Mathematical Physics}, year={2020} }

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…

## 5 Citations

### A Lieb–Thirring inequality for extended anyons

- Physics, MathematicsLetters in Mathematical Physics
- 2023

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

- Physics, Mathematics
- 2020

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

- Mathematics
- 2020

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

- Physics
- 2023

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

- Physics
- 2023

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…

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