Essential spectra of difference operators on $\sZ^n$-periodic graphs

Details Essential spectra of difference operators on $\sZ^n$-periodic graphs Essential spectra of difference operators on $\sZ^n$-periodic graphs

2007-04-18

arxiv.org/abs/0704.2268v1

Physics

Mathematical Physics

Scientific paper

10.1088/1751-8113/40/33/012

Let $(\cX, \rho)$ be a discrete metric space. We suppose that the group $\sZ^n$ acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a $\sZ^n$-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a $\sZ^n$-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on $\sZ^n$ and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures.

Affiliated with

Also associated with

No associations

Rating

Essential spectra of difference operators on $\sZ^n$-periodic graphs 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 Essential spectra of difference operators on $\sZ^n$-periodic graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Essential spectra of difference operators on $\sZ^n$-periodic graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-404622