Anyonic partition functions and windings of planar Brownian motion

The computation of the [ital N]-cycle Brownian paths contribution [ital F][sub [ital N]]([alpha]) to the [ital N]-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that [ital F][sub [ital N]][sup 0]([alpha])=[product][sub [ital k]=1][s...

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Bibliographic Details
Published in:Physical review. D, Particles and fields Particles and fields, 1995-01, Vol.51 (2), p.942-945
Main Authors: Desbois, J, Heinemann, C, Ouvry, S
Format: Article
Language:English
Subjects:
661300 > Other Aspects of Physical Science-- (1992-)
ANYONS
BOSONS
BROWNIAN MOVEMENT
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
FERMIONS
FUNCTIONS
MATHEMATICS
NUMERICAL ANALYSIS
PARTITION FUNCTIONS
QUASI PARTICLES 661100 > Classical & Quantum Mechanics-- (1992-)
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Summary:The computation of the [ital N]-cycle Brownian paths contribution [ital F][sub [ital N]]([alpha]) to the [ital N]-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that [ital F][sub [ital N]][sup 0]([alpha])=[product][sub [ital k]=1][sup [ital N][minus]1][1[minus]([ital N]/[ital k])[alpha]]. In the paramount three-anyon case, one can show that [ital F][sub 3]([alpha]) is built by linear states belonging to the bosonic, fermionic, and mixed representations of [ital S][sub 3].
ISSN:0556-2821
1089-4918
DOI:10.1103/PhysRevD.51.942