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Anyonic Partition Functions and Windings of Planar Brownian Motion

Jean DESBOIS·Christine HEINEMANN·Stéphane OUVRY
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Abstract

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

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Jean DESBOIS, Christine HEINEMANN, Stéphane OUVRY. 1994-07-13. Anyonic Partition Functions and Windings of Planar Brownian Motion. https://doi.org/10.1103/physrevd.51.942

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