Large gaps in point-coupled periodic systems of manifolds

Abstract

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.

LaTeX 2e, 24 pages

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• A "hybrid plane" with spin-orbit interaction
• On-diagonal singularities of the Green functions for Schroedinger operators
• Dynamics of an electron confined to a "hybrid plane" and interacting with a magnetic field
• Existence of spectral gaps, covering manifolds and residually finite groups
• A remark on the discriminant of Hill's equation and Herglotz functions