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.
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- Fractional quantum numbers
- Riemann orbifolds
- Holomorphic orbifolds
- Orbifold Nahm transform