Limiting Case of 1D Delta Anyon Model

David Aasen, Roger S. K. Mong, David J. Clarke +2 more

Alexei Kitaev

Ren-Gui Zhu, Wang An-Min

In order to analyze a limiting case of the 1D delta anyon model, the coupling strength of the δ interaction c is modified to become a function of the anyonic parameter κ. A pedagogic derivation of the solution for this modified model using the method of anyon-boson mapping plus Bethe ansatz is presented. The limiting case as κ → π and simultaneously c → 0, which was previously neglected, is analyzed. Some unexpected properties of this limiting case are discovered. The BAEs are compared with previous results.

S. Artz, T. H. Hansson, A. Karlhede +1 more

Anjan Kundu

A 1D Bose gas interacting through $\ensuremath{\delta},{\ensuremath{\delta}}^{\ensuremath{'}}$ and double $\ensuremath{\delta}$ function potentials is shown to be equivalent to a $\ensuremath{\delta}$ anyon gas, allowing an exact Bethe ansatz solution. In the noninteracting limit, it describes an ideal gas with generalized exclusion statistics and solves some recent controversies.

SERGEI B. ISAKOV

The equivalence of a quantum system of particles interacting with a two-body inverse square potential to a system of noninteracting particles obeying 1D fractional statistics (1D anyons), stated by Polychronakos for particles on a line, is studied for the cases where the interacting system is placed (i) into a harmonic potential on a line, and (ii) on a ring, with imposing periodic boundary conditions. In the first case, reducibility of the interacting system to the Calogero system is used to explore the statistical distribution for free 1D anyons. On a ring, the thermodynamic limit is discussed in terms of the thermodynamic (asymptotic) Bethe ansatz. Yang and Yang’s integral equation is treated in this case as describing the statistical mechanics of free 1D anyons. It gives a functional equation for the statistical distribution of 1D anyons consistent with the harmonic potential approach. We show that on a ring of a finite circumference, a system of two free 1D anyons is equivalent to a system of two particles interacting with an inverse sine square potential (the Sutherland system). We also discuss the relation to the statistical mechanics of free anyons in 2+1 dimensions.