Tuesday, April 23, 2013

1304.6028 (Ram Band et al.)

Universality of the momentum band density of periodic networks    [PDF]

Ram Band, Gregory Berkolaiko
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.
View original: http://arxiv.org/abs/1304.6028

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