Universality of the Momentum Band Density of Periodic Networks
Ram BandDepartment of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, IsraelGregory BerkolaikoDepartment of Mathematics, Texas A&M University, College Station, Texas 77843-3368, USA
2013en
ABI
Abstract
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic network. We show that this probability exhibits universal properties. More precisely, the probability to be in the spectrum does not depend on the edge lengths (as long as they are generic) and is also invariant within some classes of graph topologies.
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