Jochen Bruening, Pavel Exner, Vladimir A. Geyler
Large gaps in point-coupled periodic systems of manifolds
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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.