QUANTUM-MECHANICS ON THIN CYLINDERS

We discuss the quantum mechanics of particles of arbitrary statistics on an infinite cylinder with and without a magnetic field perpendicula r to the surface. In the presence of a magnetic field, the translation al symmetry along the cylinder is broken down to a discrete one by the Aharonov-Bohm effect. For interacting fermions in a strong field we g et an effective one-dimensional lattice model that in a limit can be m apped on an Ising chain. We also show that a system of anyons on a cyl inder are, in a certain limit, closely related to the one-dimensional (integrable) Sutherland model. By order of magnitude estimates we demo nstrate that none of these effects are likely to be experimentally obs erved with present techniques.