On the spectrum of a bent chain graph

Details On the spectrum of a bent chain graph On the spectrum of a bent chain graph

2008-07-09

arxiv.org/abs/0807.1419v2

Physics

Mathematical Physics

LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/41/41/415206

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.

Affiliated with

Also associated with

No associations

Rating

On the spectrum of a bent chain graph does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the spectrum of a bent chain graph, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the spectrum of a bent chain graph will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687823