Anyonic Partition Functions and Windings of Planar Brownian Motion

Abstract

The computation of the $N$-cycle brownian paths contribution $F_N(\alpha )$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\alpha )={\prod }_{k=1}^{N-1}(1-\frac{N}{k}\alpha )$. In the paramount $3$-anyon case, one can show that $F_3(\alpha )$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.

11 pages + 1 figure upon request

References in corpus (5)

• Equation of State of an Anyon Gas in a Strong Magnetic Field
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry
• Haldane exclusion statistics and second virial coefficient
• The Third Virial Coefficient of Free Anyons
• Topological 2-Dimensional Quantum Mechanics

Cited by in corpus (4)

• Path Integrals and Parastatistics
• One-Dimensional Statistical Mechanics for Identical Particles : The Calogero and Anyon Cases
• The fourth virial coefficient of anyons
• Virial Coefficients of Multispecies Anyons