Quantum Mechanics on Thin Cylinders

Abstract

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.

20 pages, Latex, 4 figures available on request ([email protected]), USITP-92-13

Cited by in corpus (8)

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• Mott Insulators Without Symmetry Breaking
• Emergent Kinetics and Fractionalized Charge in 1D Spin-Orbit Coupled Flatband Optical Lattices
• Symmetry breaking in Laughlin's state on a cylinder
• Jastrow-Correlated Wavefunctions for Flat-Band Lattices
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas
• Quantum Hall correlations in tilted extended Bose-Hubbard chains