Abstract
A model for the periodic system of the Aharonov-Bohm rings is constructed by means of operator extension theory. When the uniform component of the field has a rational flux through an elementary cell of the Bravais lattice of the system, the dispersion equation is found, in an explicit form. The band structure of the spectrum is studied. It is proved that under some commensurability condition the spectrum of the system consists of three parts: 1. (1) the levels of a single ring; 2. (2) the extended states; 3. (3) the bound states satisfying the dispersion equation. A physical interpretation of this spectrum structure is discussed.
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