PreprintCC BY 4.0Zenodo
Jain Sequence and Farey Hierarchy Unify Fractional Quantum Hall Topological Orders — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The fractional quantum Hall effect (FQHE) organizes its topological orders via the Jain sequence (ν = n/(2pn±1)) and a Farey-like hierarchy of filling fractions, with composite fermions as the unifying quasiparticle framework. | MATH: Jain sequence: ν = n/(2pn+1) for n=1,2,3,... (p=1 gives 1/3, 2/5, 3/7, ...). General hierarchy: ν = p/(2mp±1) with p integer. Farey mediant structure: between a/b and c/d, the next level is (a+c)/(b+d) — e.g., 1/3 and 2/5 → 3/8 (observed). The Laughlin wavefunction: Ψ_m = ∏_{i
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026jain,
title = {{Jain Sequence and Farey Hierarchy Unify Fractional Quantum Hall Topological Orders — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616619},
url = {https://zenodo.org/records/23616619},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Jain Sequence and Farey Hierarchy Unify Fractional Quantum Hall Topological Orders — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616619
UR - https://zenodo.org/records/23616619
AB - FINDING: The fractional quantum Hall effect (FQHE) organizes its topological orders via the Jain sequence (ν = n/(2pn±1)) and a Farey-like hierarchy of filling fractions, with composite fermions as the unifying quasiparticle framework. | MATH: Jain sequence: ν = n/(2pn+1) for n=1,2,3,... (p=1 gives 1/3, 2/5, 3/7, ...). General hierarchy: ν = p/(2mp±1) with p integer. Farey mediant structure: between a/b and c/d, the next level is (a+c)/(b+d) — e.g., 1/3 and 2/5 → 3/8 (observed). The Laughlin wavefunction: Ψ_m = ∏_{i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -