An exact solution for a Tan-Inkson quantum ring on a sphere gives closed-form energy eigenvalues and derived persistent currents, with curvature corrections that vanish in the flat-space limit.
Quantum mechanics and quantum Hall effect on Riemann surfaces
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abstract
The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of the $\theta$-bundle, and the wave functions of the Landau levels in the case of the the Poincar{\' e} metric. The degeneracy of the the Landau levels is obtained by using the Riemann-Roch theorem. Then we construct the Laughlin wave function on Riemann surfaces and discuss the mathematical structure hidden in the Laughlin wave function. Moreover the degeneracy of the Laughlin states is also discussed.
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A Quantum Ring in a Nanosphere
An exact solution for a Tan-Inkson quantum ring on a sphere gives closed-form energy eigenvalues and derived persistent currents, with curvature corrections that vanish in the flat-space limit.