Anyonic Partition Functions and Windings of Planar Brownian Motion

Details Anyonic Partition Functions and Windings of Planar Brownian Motion Anyonic Partition Functions and Windings of Planar Brownian Motion

1994-07-13

arxiv.org/abs/cond-mat/9407059v1

Physics

Condensed Matter

11 pages + 1 figure upon request

Scientific paper

10.1103/PhysRevD.51.942

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 $F_N^{(0)}(\alpha)= \prod_{k=1}^{N-1}(1-{N\over k}\alpha)$. 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 $S_3$.

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