Dual families of non-commutative quantum systems

Details Dual families of non-commutative quantum systems Dual families of non-commutative quantum systems

2005-02-16

arxiv.org/abs/hep-th/0502143v1

Phys.Rev. D71 (2005) 085005

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, no figures

Scientific paper

10.1103/PhysRevD.71.085005

We demonstrate how a one parameter family of interacting non-commuting Hamiltonians, which are physically equivalent, can be constructed in non-commutative quantum mechanics. This construction is carried out exactly (to all orders in the non-commutative parameter) and analytically in two dimensions for a free particle and a harmonic oscillator moving in a constant magnetic field. We discuss the significance of the Seiberg-Witten map in this context. It is shown for the harmonic oscillator potential that an approximate duality, valid in the low energy sector, can be constructed between the interacting commutative and a non-interacting non-commutative Hamiltonian. This approximation holds to order 1/B and is therefore valid in the case of strong magnetic fields and weak Landau-level mixing.

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