Anyonic Partition Functions and Windings of Planar Brownian Motion

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 1994-07
Main Authors: DESBOIS, Jean, HEINEMANN, Christine, OUVRY, Stéphane
Format: Article
Language:English
Subjects:
Brownian motion
Coils (windings)
Numerical analysis
Partitions
Partitions (mathematics)
Random walk
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 \(S_3\).
ISSN:2331-8422
DOI:10.48550/arxiv.9407059