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arXiv · 2505.23127

Two identical 1D anyons with zero-range interactions: Exchange statistics, scattering theory, and anyon-anyon mapping

Raúl Hidalgo-Sacoto·Thomas Busch·D. Blume
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Abstract

While elementary particles obey either bosonic or fermionic exchange statistics, generalized exchange statistics that interpolate between bosons and fermions -- applicable to quasi-particles -- constitute an intriguing topic, both from the fundamental and practical points of view. This work develops a scattering framework for two identical 1D bosonic anyons and two identical 1D fermionic anyons with zero-range contact interactions. The two-body system with zero-range interactions, both in free space and under external confinement, is used to illustrate the recently proposed bosonic-anyon -- fermionic-anyon mapping~(R. Hidalgo-Sacoto {\em{et al.}}, arXiv:2505.17669), which connects the eigenstates of bosonic anyons to those of fermionic anyons and vice versa. Performing explicit calculations for two-particle systems, the momentum distributions and the off-diagonal correlations of the single-particle density matrix for bosonic anyons and fermionic anyons are confirmed to be distinct. We also confirm the previously derived asymptotic coefficients of the momentum distribution tail at orders $k^{-2}$ and $k^{-3}$ for two harmonically confined anyons. Non-universal contributions at order $k^{-4}$ are discussed.

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Raúl Hidalgo-Sacoto, Thomas Busch, D. Blume. 2025-05-29. Two identical 1D anyons with zero-range interactions: Exchange statistics, scattering theory, and anyon-anyon mapping. https://arxiv.org/abs/2505.23127

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