Large gaps in point-coupled periodic systems of manifolds

Details Large gaps in point-coupled periodic systems of manifolds Large gaps in point-coupled periodic systems of manifolds

2002-12-18

arxiv.org/abs/math-ph/0212052v1

J. Phys. A36 (2003), 4875-4890

Physics

Mathematical Physics

LaTeX 2e, 24 pages

Scientific paper

10.1088/0305-4470/36/17/314

We study a free quantum motion on periodically structured manifolds composed of elementary two-dimensional "cells" connected either by linear segments or through points where the two cells touch. The general theory is illustrated with numerous examples in which the elementary components are spherical surfaces arranged into chains in a straight or zigzag way, or two-dimensional square-lattice "carpets". We show that the spectra of such systems have an infinite number of gaps and that the latter dominate the spectrum at high energies.

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