Quantum Mechanics on Thin Cylinders

Details Quantum Mechanics on Thin Cylinders Quantum Mechanics on Thin Cylinders

1993-01-14

arxiv.org/abs/cond-mat/9301018v1

Physics

Condensed Matter

20 pages, Latex, 4 figures available on request (wes@vana.physto.se), USITP-92-13

Scientific paper

10.1103/PhysRevB.47.16554

We discuss the quantum mechanics of particles of arbitrary statistics on an infinite cylinder with and without a magnetic field perpendicular to the surface. In the presence of a magnetic field, the translational symmetry along the cylinder is broken down to a discrete one by the Aharonov-Bohm effect. For interacting fermions in a strong field we get an effective one-dimensional lattice model that in a limit can be mapped on an Ising chain. We also show that a system of anyons on a cylinder are, in a certain limit closely related to the one-dimensional (integrable) Sutherland model. By order of magnitude estimates we demonstrate that none of these effects are likely to be experimentally observed with present techniques.

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