Abstract
We study the quantum dynamics of a particle bound on a torus in the presence of an external magnetic field. We derive and discuss the effective Schrödinger equation for the surface eigenmodes and the corresponding quantum effective potential which is periodic and exhibits quantum anti-centrifugal force for non-vanishing angular momentum quantum numbers. An energy band structure of pure geometrical origin emerges naturally which can be tested experimentally in semiconducting as well as carbon nanotori.
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