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Type: Journal article
Title: Fractional quantum numbers via complex orbifolds
Author: Mathai, V.
Wilkin, G.
Citation: Letters in Mathematical Physics, 2019; 109(11):2473-2484
Publisher: Springer Nature
Issue Date: 2019
ISSN: 0377-9017
Statement of
Varghese Mathai, Graeme Wilkin
Abstract: This paper studies both the conductance and charge transport on 2D orbifolds in a strong magnetic field. We consider a family of Landau Hamiltonians on a complex, compact 2D orbifold Y that are parametrised by the Jacobian torus J(Y) of Y. We calculate the degree of the associated stable holomorphic spectral orbibundles when the magnetic field B is large and obtain fractional quantum numbers as the conductance and a refined analysis also gives the charge transport. A key tool studied here is a nontrivial generalisation of the Nahm transform to 2D orbifolds.
Keywords: Fractional quantum numbers; Riemann orbifolds; holomorphic orbibundles; orbifold Nahm transform
Rights: © Springer Nature B.V. 2019
DOI: 10.1007/s11005-019-01190-y
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